Well, houses do run in families, but I always believed it was more a matter of nurture than nature.  Members of the same families just tend to have the same values and personality traits.  The New From JK Rowling bit on the hat in Pottermore states that it selects students through its own judgement, and using its skills in Legilimency.  There's no mention of it being capable of tracing Genealogy.

I don't think Slytherin is right anyway.