It would be interesting to know when this conversation took place, Rob. Late in his relatively short life Garry began to lose contact. As you probably know, after he died 2,500 undeveloped rolls of his film turned up. If you look at his later work you see that what he was saying about the narrative ability of photographs applied to most of his own work at that time, though there were a few gems among the stuff. But I agree with him that a shot has to be complete within the frame. That's one problem I often see over in User Critiques, a frame that's not complete within itself. Don't misunderstand what I'm saying. Garry is one of my all-time favorite photographers. Some of his earlier work is astonishing, and contains loads of narrative information. Anybody who wants to do street photography would be well advised to become intimately familiar with Garry's work.
I love the story about the time he was lecturing to a group of museum curators. He had, I think, this photograph projected on the screen:
http://adequatebird.com/wp-content/uploads/2011/05/Garry-Winogrand-imgSrv_020.jpg. With his nose in the air, one curator who didn't really think of photography as art asked, "Mr. Winogrand, how long did it take you to produce this 'work of art?'" Garry turned around and looked at the picture for a minute and then said, "I think it was 1/100th of a second."