USA - is it really legal to run a red light at right turn?

On ATS the traffic often ignores the red light and makes a right turn. I thought it was a bug, so I reported it to SCS Software but they said it was legal in America to run a red light at right turns. I asked a few different groups of Americans on Facebook (back when I still had an account on it) and they all said it was true. But this makes zero sense to me bc if it's legal to ignore the red light, then what's the point of having a traffic light at all? Not to mention that this is a perfect cause for a traffic accident. If there's a vehicle coming from your left and you don't see it (or they don't see you), there's gonna be a crash. And then I find this image below.

So which is it in the end? Is it legal or is it not legal to make a right turn at red light in America? If it is legal, what's the logic behind it?

USA - is it really legal to run a red light at right turn?
USA - is it really legal to run a red light at right turn?
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