OpenAI's board's press release could very easily be construed as "Sam Altman is not trustworthy as a CEO", which could lead to his reputation being sullied among other possible employers. He could argue that the board defamed his reputation and kept him from what was otherwise a very promising career in an unfathomably lucrative field.
Really they should have just said something to the effect of, "The board has voted to end Sam Altman's tenure as CEO at OpenAI. We wish him the best in his future endeavors."
When you're a public person, the bar for winning a defamation case is very high.
Also, as long as you are a public person, defamation has a very high bar in the USA. It is not enough to for the statement to be false, you have to actually prove that the person you're accusing of defamation knew it was false and intended it to hurt you.
Note that this is different from an accusation of perjury. They did not accuse Sam Altman of performing illegal acts. If they had, things would have been very different. As it stands, they simply said that he hasn't been truthful to them, which it would be very hard to prove is false.
Surely, at some level, you can be sued for making unfounded remarks. But then IANAL so, meh.
No, in the UK it's unambiguously the other way round. The complainant simply has to persuade the court that the statement seriously harmed or is likely to seriously harm their reputation. Truth is a defence but for that defence to prevail the burden of proof is on the defendant to prove that it was true (or to mount an "honest opinion" defence on the basis that both the statement would reasonably be understood as one of opinion rather than fact and that they did honestly hold that opinion)