Greg was not invited (losing Sam one vote), and Sam may have been asked to sit out the vote, so the 3 had a majority. Ilya who is at least on "Team Sam" now; may have voted no. Or simply went along thinking he could be next out the door at that point; we just don't know.
It's probably fair to say not letting Greg know the board was getting together (and letting it proceed without him there) was unprofessional and where Ilya screwed up. It is also the point when Sam should have said hang-on - I want Greg here before this proceeds any further.
Do things work differently in America?
> at least four days before any such meeting if given by first-class mail or forty-eight hours before any such meeting if given personally, [] or by electronic transmission.
But the bylaws also state that a board member may be fired (or resign) at any time, not necessarily during a special meeting. So, technically (not a lawyer): Board gets majority to fire Sam and executes this decision, notifying Mira in advance of calling the special meeting. During the special meeting, Sam is merely informed that he has been let go already (is not a board member since yesterday). All board members were informed timely, since Sam was not a board member during the meeting.
If Ilya was on the side of Sam and Greg, the other 3 never had a majority. The only explanation is that Ilya voted with the other 3, possibly under pressure, and now regrets that decision. But even then it's weird to not invite Greg.
And if the vote happened in an illegitimate way, I'd expect Sam and Greg to immediately challenge it and ignore the decision, and that didn't happen.
On the board that I was on we had normal matters which required a simple majority except that some members had 2 votes and some got 1. Then there were "Supermajority matters" which had a different threshold and "special supermajority matters" which had a third threshold.
Generally unless the articles say otherwise I think a quorum means a majority of votes are present[1], so 4 out of 6 would count if the articles didn't say you needed say 5 out of 6 for some reason.
It's a little different if some people have to recuse themselves for an issue. So say the issue is "Should we fire CEO Sam Altman", the people trying to fire Sam would likely try to say he should recuse himself and therefore wouldn't get a vote so his vote wouldn't also count in deciding whether or not there's a quorum. That's obviously all BS but it is the sort of tactic someone might pull. It wouldn't make any difference if the vote was a simple majority matter and they already had a majority without him though.
[1] There are often other requirements to make the meeting valid though eg notice requirements so you can't just pull a fast one with your buddies, hold the meeting without telling some of the members and then claim it was quorate so everyone else just have to suck it up. This would depend on the articles of the company and the not for profit though.
So the support was very thin and this being a controversial decision the board should have sought counsel on whether or not their purported reasons had enough weight to support a hasty decision. There is no 'undo' button on this and board member liability is a thing. The probably realize all that which is the reason for the radio silence, they're just waiting for the other shoe to drop (impending lawsuit) after which they can play the 'no comment because legal proceedings' game. This may well get very messy or, alternatively it can result in all parties affected settling with the board and the board riding off into the sunset to wreak havoc somewhere else (assuming anybody will still have them, they're damaged goods).