I think part of it is the "correct" response to Harry's fears just seems so obvious. Like, even if Dumbledore wants to stress that Harry should never worry that he's "supposed" to be anything when he makes himself what he is, it seems like of course he should first say that being put in Slytherin would not have made Harry a bad person. He'd be just who he is now, in a different color tie. It's just hard to think that any headmaster would stand for someone ccasually assuming that being put in one house makes you a bad person. In these days of political correctness it just seems like a no brainer.

Maybe JKR doesn't have Dumbledore say this because she's planning to *show it* in later books, or maybe we really are supposed to think of the house just the way Harry does. It's just that second possibility is very hard to do.