You were right the first time - it provides the character with an extra Story Point.
It's a Special Bad trait. But, as written, there is no character point bonus for having it. It's never been pointed out as an error so far as I know, so I think that's correct - the character just gains a Story Point.
Ah ok. Sorry, I just happened to also see that trait in the Second Doctor book and it said "costs a Story Point" and it got me flipped around.