Insisting, no matter how painful, that the organization stays true to the charter could be considered a desirable trait for the board of a non-profit.
Instead of "Sam has been lying to us" it could have been "Sam had diverged too far from the original goal, when he did X."
They could have meant that Sam had 'not been candid' about his alignment with commercial interests vs. the charter.
If Sam returns, those three have to go. He should offer Ilya the same deal Ilya offered Greg - you can stay with the company but you have to step down from the board.
In the initial press release, they said Sam was a liar. Doing this without offering a hint of an example or actual specifics gave Sam the clear "win" in the court of public opinion.
IF they would have said "it is clear Sam and the board will never see eye to eye on alignment, etc. etc" they probably could have made it 50/50 or even favored.