Indeed. But I don't think anyone is saying that. My take on it starts with the notion that the human mind is, among other things, a machine for inventing and finding stories. Google "narrative psychology" for pages and pages of references in a variety of fields. Put simply, we look for and find stories in the world around us, including on the streets, and including in photographs. Photography (and visual art generally) hooks into this quality of the mind in a variety of ways. Documentary photography, as Russ has described it, as a common way. Obama's inauguration, a mother and baby, the audience at a rock concert - you get the idea. It is worth noting that you have to know the story before you can find it and many stories are more or less culturally specific. To a member of an undiscovered tribe in the upper Amazon, a picture of Obama's inauguration probably wouldn't tell much of a story but they would probably get the mother and baby. To me, a photograph of a landscape in Central Australia is just another landscape, while to an aboriginal person who lives there it will tell a detailed story about creation myths and the songs in which they are remembered.
Sometimes, though, there has to be a story there, but we can't work out quite what it is. "Ambiguity", as I have argued before, and as Russ has agreed, isn't at all a good word for this because, as you rightly say, it implies two or more identifiable meanings which you flip between and that absolutely isn't what we are talking about. It has, however, been the word used in many conversations about photographs which have the quality we are talking about, because nobody has come up with a better one. It isn't a matter of making up a variety of possible dialogues arbitrarily as you suggest. The image asks for a narrative answer, even demands one, and constrains, through its content, the possible answers, but refuses to conclusively provide one - but we can't let it drop, because the image is powerful enough to suck us in. It's not that you make up stories, rather that the image asks the question "what exactly is going on here" and you can't quite get to an answer. This is an experience which you may or may not have had. If you have had it you know what we are talking about.
I agree with you that "ambiguity" in this sense is just one possible quality in photographs of people out of doors and isn't in any way synonymous with quality. But I am a bit surprised that you go on to say that you have never heard of anyone regard it as synonymous with quality. When you denounce those of us who value "ambiguity" as being stuck in the past and talk about how young street photographers are doing different and fine things, you seem to imply that we think that "ambiguity" is the only way to do photography of people out of doors. I think most of us don't, and we we mostly agree about the young street photographers as well. And if you want to talk about the past, google "Cartier Bresson Images" and look through what you find. I just did this and concluded that many, even most, of the shots I found were primarily documentary. But some had this other quality, to a greater or lesser degree. If we could sit down together in front of a screen, we could have a friendly discussion about where we found it. I find it, for example, here - and note that people looking out of the frame is a common feature, because you wonder what they are looking at.
It's good and well to be done with ambiguity. I think even RSL has dumped it. Let's move on. I conclude you also didn't buy Chris' answer, because it really just involved alternate dialogs he supposed were possible, and which made it ambiguous to him. Even if you don't reject that, I do. Ok then, you go on to describe this certain something you are all looking for. If I reduce it down, I'd say you are describing the quality of mystery and enigmatic narrative. I will now argue that such is so common it doesn't deserve this high place you have set aside.
Let me start by countering RSL's latest rule that the photograph (for this genre) "can't be self explanatory." This is the replacement for ambiguity. This new rule is in clear conflict with the very essence of photography, which is that ALL photographs are both self-explanatory, self truthful, and self-contained. More to the point, the photograph is an explanation of time and space itself. A thing which can't explain itself can not therefore be a photograph. But that statement doesn't carry with it the idea that every viewer will understand or accept the explanation offered in the photograph. The photograph IS...whilst the viewer APPROACHES. The viewer doesn't bring truth the photograph. The truth existed before it was viewed. This is inviolable. So, when a photograph makes a person dream various dreams, think various thoughts, and feel various emotions, it is the truth of the content causing those effects. All photographs do that by degree. Not just street photographs, and not just "these certain special kinds" of street photographs. There is nothing special at all about a photograph stimulating multiple dreams and visions in certain people. The one that does it for you, may not do it for me. Well, these things are obvious I won't detail all the permutations.
When you engage a photograph, you can ponder a thousand questions. Who, what, why, when, where? And for each character, each face, each circumstance. The more the photo engages you, the more questions you can ask, if you like doing that. Or you can search for the truth that the photograph is expressing within itself. That might involve no questions. One approach is not better or worse than the other. They are different. I can easily suggest that just keeping your mind occupied with a thousand questions about who'dunnit, might mean you miss the explanation all together. Then you get into how to access the truth in a photograph. A very individual thing. BUT, whatever that questioning is about, it doesn't define the importance of a photograph. You can't say, "this one creates more questions, and thus is a better photo." That should not be arguable.
The inherent power of photography is that stimulation which happens because the photograph is a truth unto itself. The viewers are all out there peering into these truths, and quite frankly, most of the time they are scratching their heads. A guy asked me in the "Travel Vista" thread why on earth I posted some of those photos. He said, try as he might, he couldn't find a reason I would post them (keep in mind this was a photographer asking). What's the meaning there? Here's how I explained it to him. If I write on the chalk board "F=ma", and then ask the assembled audience, "What is this explaining?" Or, "what truth is being expressed there?" I will get some who know what it means, and some who don't have a clue. The difference in the two groups is: background.
I have been studying photographs for 45 years. I am well familiar with the photographs of all the renown photographers. What I know for certain is that there are only three paths by which a viewer finds interest (connection) in any of those photographs: by intellectual introspection; by emotional connection; by visual stimulation. Some viewers of a particular photograph get one path going, some get all three, and many get none. The difference is: background.
The summary is this. If your background is stuck at Cartier-Bresson (name your artist), you will connect only to those themes and styles and features of those photographs. Tell me you haven't heard a parent of a 16 year old saying, "That crap is not music!" If your background is stuck on enigmatic photographs, then direct one might not make sense to you. Art simply doesn't stand still for anyone though and what was before is simply past.
I look at contemporary photography all the time, every day. I am part of intensive personal critiques with artists and photographers weekly. I am not stuck in any photographic era, or stuck on any photographic artist. It's today, I am going to take my own photographs, which will contain their own truths and explanations. I did pay my dues to all those who came before, and they all said the same thing: be true to your own vision. It might be gawd-awful, but it is mine and not borrowed. Never once before pressing the shutter button have I stopped to ask myself, "Is this how the other guys would do it?"
I am always enjoying looking at photographs. If you'd like to look at some together (somehow), It's one of my favorite pastimes. I'm always game. Thanks.