Well, the other time the stats - be they good or bad - seem to make a difference is when the player takes them to heart and in effect decides to allow them to make said difference in the approach to how the character is played.
For example, a player who rolls really good stats might decide to underplay the character to bring it down to the party level - and in so doing run it into the ground as an unintended side effect. Or on the flip side, a player with god-like stats might decide to overplay the character as a one-person show and either become the party MVP or (more likely) die trying. Either way, the stats have influenced the play beyond just what the numbers say - and I've seen both happen (and done the second one myself, dammit!).
Going the other way, a player whose character's stats are somewhat limited might decide that the character is worthless and play it as such - contributing nothing instead of what it can - thus making it even less useful than it otherwise might be. Again, an example of the numbers influencing the player's approach above and beyond the simple math effects.
Take the example of Tik and the hell hound a few posts up. Tik's player could get discouraged, decide that Tik is both worthless and hopelessly outgunned, not put any thought or effort into keeping her going, and let Tik quietly die the death. Or, Tik's player - knowing full well that Tik's odds aren't great - could get on the front foot and have her stand in nonetheless to give it everything she has, and cheer her on knowing what a great story it'll be if she wins!
Lan-"I've played Tiks in the past - they don't always last long, but when they do it's wonderful"-efan