Nobody disputes that the apartments are walking distance from Union Square - albeit a crappy walk that makes it feel more removed than it is distance wise. The problem is that a lot of businesses in the area actually use Union Sq in their address. This makes sense seeing that it can be confusing to determine what street they are on due to the layout of the area, not to mention the fact that unlike these apartments all these businesses are you know, *in* the square. Casa B, for example, could justify using "Union Sq" instead of a street though interestingly they still say Washington St.
The apartments at "197 Washington" however have no such confusion associated with where it is, and thus has no justification to make up fake addresses as a marketing gimmick. Clearly somebody thought "you know this Union Square is gonna be a hip new gentrifying place so let's get it in our name somehow!" It's almost as if they are worried that the apartments might seem too distant if they don't really drive home the point - "no really, I know it looks like shitty overpasses and busy wide roads but I swear Union Square is just around that bend! We even put it in the name!"
It's going to get even more confusing when the two T stops open and this one is way closer to "Washington" and not "Union".