The reality: You can't take shareholder money out on the front lawn and set it on fire
What the internet thinks: Company not only can do insert shitty thing here but MUST do insert shitty thing here because they have a fiduciary duty.
The problem is that the internet perception of reality is semi fictional. They damn well could have simply stated that they as a company don't take a personal position on Tibet but wont be bullied and faced near zero chance of successful lawsuit even if investors took a short term bath due to business in china.
To refute this simply provide examples of investors who successfully sued because of decisions they didn't agree with an explain how this situation is similar.
Mandated by what law? What if Marriott determines that long-term goodwill in their brand is what's in their shareholders' best financial interests?
I don't think "letting" is a very accurate word in this case — Marriott could pull out of China (likely at a loss) but the company doesn't want to because it would be financially stupid. In fact, as a public company Marriott is mandated to act in its shareholders' best financial interests.