There's a big difference between smoothing out dialogue (taking out the repetitions and fillers, etc.) and just making things up.
I'd say there is also a rather large area in-between these two. More the point, I'd say that the distinction is more important in other types of writing. If he had been writing an article for a newspaper, let's say, in which he was writing an expose on homelessness in his city, then I would expect him to capture the essence of Joe's words as accurately as possible, and for Joe to be real. Mostly, that's because then he would be writing a piece in which his stated purpose would be to write a story that was true to Joe. In this case, though, his stated purpose, or rather, the one that was given to him, was
The essay must make a point about something you've learned or realized.
It must be based on your personal experiences which have occurred in the last few years.
To me, that puts the essay firmly in the "creative" realm. Just think about how many Hollywood movies are "based" on true stories, yet have huge swaths of the material completely made up. All he has been asked to do is to capture a lesson that he has learned based on his personal experiences. Under such circumstances, Joe might easily be a composite of several homeless people he had met, with the incident emblematic of the larger truth he wishes to convey, rather than either Joe or the incident being "real," in the sense you seem to mean.
I'm not trying to convince you, btw, only to clarify my own stance. I suspect that this is a case where we will have to agree to disagree. That's okay, though -- it would be a dull world indeed where people were always in accord.