Whether Dean lives without Sam or dies without him, he's still going to lose him, so Billie's implication that Dean's desire to save Sam is simply motivated by the selfish need to keep him around is, at the very least, not the whole story. I just don't think we should accept everything that's said on the show at face value. There are a lot of commonly repeated myths, that are even accepted as facts by the characters themselves, that are actually contradicted or at least called into question by the action we've actually witnessed if we're paying attention.