I disagree with the person who declined the flag. That post needs to be removed.
The simple answer to your headline question is moderators or in some circumstances the community. If someone uses the 10k tools and disputes a flag that can negate it, though in this particular case that wouldn't have happened as I don't think offensive flags are shown to the community.
When dealing with flags we generally asses their validity based on the type of flag. I believe it was correctly declined as it was flagged as Offensive, it may offend your professional sensibilities but it's not offensive in the meaning of that flag. An Offensive flag against someone carries a larger penalty than normal too.
If it had been flagged as Other with commentary that it's a truly awful answer that the internet is better off without then it probably would have been removed, no guarantees though, we're closely aligned but not always in full agreement.
Equally, some members of the community would prefer to see hugely downvoted answers left hanging at the gates as a warning.