I don't think this has anything to do with trust. It's absurd not to trust Huang as the best possible CEO for the company that he brought from zero to 5 trillion dollars in value. It's about being afraid of public opinion, and especially fear of being blamed for not taking the expected decision.
But.
He put together a string of frankly insane mistakes that are now endangering that 5 trillion dollar company from both the inside and outside. There's no chance in hell that they're going to go from $5T back to 0, but you are not understanding the trouble they're in.
Internally, boinking your direct reports (who also happened to have a string of recent promotions) is incredibly ruinous to a company's internal culture, destroying notions of internal meritocracy. How would you feel if all your hard work was apparently not as important as putting out for the CEO? Do you think that would make you eager to do your best work for that CEO? And that's even before thinking about the insane legal liability.
Externally, he got honeypotted by a foreign government and managed to simultaneously mess with national security and, it seems, circumvent export controls to the tune of tens of billions of dollars. nVidia is in some extremely serious shit, and will have the government breathing down their necks between now and the end of time.
Huang betrayed 38 years of trust his wife put into him and recently betrayed the Board by lying to them. That's already admitted, no ifs or buts. He clearly had reasons, as he is a sane person. His reasons were romantic engagement with (alleged) spy. Since he is a sane person, he must have weighed pros and cons and still engage in an affair, even though it jeopardized his marriage and his job. The Board needs to do bunch of "what ifs" in such situation, including paranoid ones, such as "what if this woman had such access to NVIDIA tech stack that each cheap is infused with some form of Chinese virus". We simply don't know how far this goes, but this firing certainly shows much further than just a consequence of a romantic fling.