It isn't a matter of should. But they definitely could, if Binance operates in Iran, and they suspect Binance is doing something that is against the law there.
>And if they do, why is it Binance responsibility to bow to the Iranian government?
If they want to conduct business with Iran, then they have to take on that responsibility. If they don't care about conducting business with Iran, they are welcome to not listen to any demands and just walk away.
>And if they don't bow, why should Binance bow to the US?
If they don't bow, they won't be able to conduct transactions and business with US entities completely, such as banks and payment providers. Whether they should bow or not is up to whether they want to continue that relationship.
For context, Binance DOES operate within the US, they just have a separate entity set up for it called Binance US that is fully compliant with US regulations and doesn't allow trading crypto derivatives (only regular crypto coins). Binance (the non-US one that allows derivatives) is self-blocking US users. The allegation is that despite all of that, Binance allowed derivative crypto trades to slip through the cracks in the US.
If Binance doesn't comply and is at fault, then they are risking getting their Binance US entity prevented from operating in the US. This has nothing to do with world policing or anything like that. If the business you are conducting in a country doesn't comply with local regulations, you are running a risk of getting investigated and asked to either fix it up (if you were given such a chance depending on circumstances) or get out, as simple as that.