Is it okay for a moderator to ban a user for being abusive?

Is it actually within a moderator's rights to hand out a ban if someone decides to get personal and start hurling insults?
I don't hang out on this specific forum all that much, even though I honestly have a pretty high opinion of the site, the quality of the content, and how things are run here.
I’m curious to hear what the moderators and the rest of you users think about the situation, and whether there's an official stance on it, since I couldn't quite pin down a definitive answer while digging through the rulebook.
The guidelines just vaguely state that being generally abusive toward other members is against the rules, but that's about it.

A moderator absolutely has the right—and honestly, the responsibility—to step in and issue sanctions whenever someone starts being abusive on a thread they’re overseeing, regardless of whether those insults are aimed directly at them or just directed at another user in the community.

rustydrifter10 said:A moderator has every right—and honestly, an obligation—to step in when someone starts throwing insults on their board, whether those attacks are aimed directly at them or just some random user elsewhere in the thread.

Yeah, that’s exactly what I figured, but apparently, I’m the crazy one because some people in another thread are insisting it works differently.

Daniel Wilson6 said:Yeah, that’s what I was thinking too, but honestly, I had someone in another thread insisting it works differently.

Wait, who exactly is telling you that? 🙂 Look, the mods on some random subreddit might make a backroom deal to swap out who issues a ban if one of them feels personally attacked, but that isn't some kind of universal rule.

rustydrifter10 said:Who on earth told you that? 🙂 Just because a few mods on some random internet message board might collude to ban someone just because their feelings got hurt doesn't mean that’s how things work everywhere.

Look, I used to be a moderator on another forum, and I’ve been doing this a long time, so I actually know what I'm talking about. That’s why I was genuinely taken aback and decided to head over here to ask the biggest, most established community I know in America.