[jholman]

btilly's comment is exactly correct (though obviously not a complete explanation of everything).

The S.O. link you posted contains an Accepted Answer which is also exactly correct, and happens to agree exactly with btilly.

I don't know what you think you're saying, or what you think that SO link supports. But it is NOT the case that "big O is worst-case", nor is it the case that the variants like little-o/big-theta/big-omega/etc have anything to do with best/worst/average case. The relevant sense of "upper bound" is not some kind of subtle synonym for "worst case".