You don't stop performing until somebody switches your mic off, you keep going - stopping early can result in audiences turning or panicking even more. Depending upon the actual lighting rig/setup, there's a good chance you can't see more than the odd glimpse - your world is what you can see and that is the stage. There's people employed to deal with the crowd, it's not anything to do with you, your job is to be on that stage and perform.
Stage intruders aren't always telling the truth or safe. The only people you can trust are those who you know are supposed to be on stage and the voice in your earpiece - and asking 'who?' is completely normal in that circumstance, as you have to know if it's somebody giving an instruction that has the authority to do so or whether it's somebody who doesn't - it'll cost thousands if not more (personally, too - performance contracts are very strict) if you stop and it wasn't an official instruction from somebody with authority; again, not being able to see a great deal whilst on stage is relevant here.
Yeah, I'm sure he's a dick. But when shit is going down, you're often the last to know that there's a real problem, as it's not your job. Your job is to stand up there in a pool of bright light, make noise and look good. And there will be extremely angry owners, promoters, agents, tech team, security team, etc, if you overstep and make decisions about things you don't know, can't see and you are not qualified to do so with.
People are conflating what appears to be an utter clusterfuck of crowd behaviour plus crowd, venue and security management with the performer's job. Which is to perform.