What's more likely, I think, is that the CEO meant was that if he declined the offer, the board may fire him and replace him with someone who won't decline it. So if it's an eventuality either way, he may as well be the one to lead it.
While that isn't true, if a corporate board takes actions that are contrary to shareholder interest, they open themselves to liability. In the case the GP is talking about, where a buyout offer exceeded any amount of return that the company could possibly provide while remaining independent, shareholders would absolutely have a case if that acquisition offer had actually been turned down.
If one can't cite a specific US code, it's not a legal obligation. It could be in a charter or contract, but it's not US law. Feel free to correct me if you can cite one. I believe this is a good starting point: https://www.congress.gov/advanced-search/legislation
Fiduciary duty doesn't apply to most non-finance related companies. It's mostly something that investment firms are required to do. And you'll know if you become their client. If Google is doing that they definitely need broken up. It means they have a duty to use your money to make more for you, and not lose any if possible.
Likewise I have yet to hear a coherent legal justification for the idea of the "state monopoly on violence" that doesn't boil down to a just-so story invoking the fiction of the social contract (even the US only grants a limited exemption to this via the second amendment and even that still uses the context of "militias"). But even in Civil Law systems that doesn't mean the state won't act as if it is a thing and base legislation on that assumption.
See, for example, Section 5231 of the California Corporations Code.
https://codes.findlaw.com/ca/corporations-code/corp-sect-523...
Which boils down to the same thing. Incorporate where it's not. Viola - no legal obligation.