You're absolutely right, Andrew. A picture of a street, literally, is a street photograph. But if we accept that usage, then the term "street photography" becomes meaningless as a name for a photographic genre and the genre disappears. I'd hate to see that happen because as far as I'm concerned real street photography tops the list of things for which a camera is useful. Maybe we could come up with a better term for capturing meaningful human interaction to take its place.
Here's a quote from my essay "Why Do Street Photography?" I stand by it:
"Nowadays we can look at the photographs of Eugene Atget and learn something about the people who lived in his time and in his surroundings, but the most effective glimpse of historical human differences comes not from the kind of documentary photography possible with Atget's slow view camera and his posed subjects, but from the kind of street photography that became possible with the introduction of the small hand camera. Oskar Barnack's 1925 Leica finally made it possible for artists like Andre Kertesz and Cartier-Bresson to photograph people as they were, in an uninterrupted state, rather than as they were when posing.
"An historical novelist guesses at the past on the best evidence he can find, but a photograph isn't a guess; it's an artifact from the past that has captured time. And so, a street photograph that has captured not only the visages of its subjects, but the story that surrounds their actions can be a more convincing reminder of how things were than any novel or any straight, posed documentary photograph."