In three years on this site, this is the most surprising difference in use of English I have discovered.
I can entirely see how "it just about killed me" would be a negative but mainly because it's so unlikely that it actually would kill you and, if it had, you wouldn't be around to utter those words!
However, with "real" situations and descriptions, I can't think of a single instance in which it's a negative.
He's just about tall enough to reach the top of the cupboard = He can get his fingertips on top of the cupboard by stretching to his fullest possible extent.
I have just about enough rice to make a risotto = I need 300g of rice and I have 301g. Phew! I don't have to go shopping for rice. (We would also say, of course, "I have just enough rice ..." to mean the same thing.)
Was thinking more about this.. it could mean "just over the amount needed" in this context:
I've had just about enough of you. (But even then, it still could mean "watch out, you're about to cross the line")
But, to my ears, there is a clear distinction here:
We have just enough people to get started, so now we can begin.
We have just about enough people to get started, so let's wait another minute, then we'll begin.
It's a way of introducing a little uncertainty into an otherwise boring definite outcome of whether it was or it wasn't wide enough. The little uncertainties can sometimes be more interesting...
Phrases like "just about", "nearly" and "almost" also have this peculiar aspect of triggering a mental picture in your mind's eye.
OP, did you not imagine yourself holding one hand up to your face with thumb and forefinger about an inch apart as you read the segment, "the bench was just about wide enough"?
PS: I also agree with ems that it's one of the most surprising differences I've come across here too. I would not have guessed it.