As much as on paper they aren't the board's boss, based on how events turned out they effectively were. They had leverage over the board to get what they want.
I agree that the board overestimated their own power, and underestimated the need to get their business partners on board with Altman's firing. However, I think calling Microsoft the board's boss implies that Microsoft has some sort of moral or legal high ground.
One way this debacle has been portrayed in the media is "an unaccountable board tried to destroy a profitable company". I think a more accurate portrayal is "Sam Altman and Microsoft worked together to deemphasize the company's scientific and humanitarian goals and emphasize building successful and profitable products". It's sort of depressing how Microsoft was able to "capture" a nonprofit.
I think it's not as much that Microsoft is their boss or not, it's that no one considered the board to be the boss of OpenAI. That's why we saw so many employees wish to leave when they fired Sam Altman.
