In reality, there was no decision to fire AVB.
Rather, it was a textbook example of someone's position becoming untenable.
It is still speculation to an extent, but the version of events that rings truest to me is that Levy and Baldini hadn't planned to sack AVB on the Sunday after the Liverpool game. Rather, they went to AVB after the game to ask what was going on and found him brusque and intransigent to their questioning. They all slept on it, and it was only on the Monday when they met and nobody could back down that the end came, at which point not even AVB himself put up much fight to stay.
The reason I believe that general outline to the story is because it's so similar to what happened at Chelsea. Results, performances, personal relationships, squad harmony, trust between employer and employee, fan relations, media relations...all were shot to pieces at both Spurs and Chelsea, whatever the rights or wrongs on either side. Maybe AVB was right in both instances, but if you can't manage the politics and personal relationships, being right isn't enough and your position eventually, inevitably becomes untenable.
The mistake wasn't sacking him, it was hiring him in the first place.