My read on it was following the board's extended review of club operations they lined up Vinai as Levy's successor and he acted as their puppet and mouth-piece over the summer.I do not think Vinai had much influence until Levy left but yes the board made the decision but it is not clear if the sacking was supported by Levy. I do not think any decision on next season has been made and it will depend on results and the reactions of the home fans. If the atmosphere is like recent matches then he will go. It is rumoured that at least 1 board member wants Frank out and whatever Vinai believes if things do not improve he is gone.
While it's impossible to know for sure, I suspect Levy was on a much shorter leash than in previous years. Donna Cullen getting axed, chummy PR wine-chats with Vinai, us spending far more on wages for Xavi than Levy would typically condone, the 'collective' sacking of Ange - it wasn't a typical summer by Spurs and Levy standards.
As for whether Levy supported the sacking of Ange, I wouldn't be surprised if you're right. I could see Levy succumbing to the emotional fan-reaction post-Bilbao and deciding to keep him. The fact the statement specifically name-checked the board does seem like Levy trying to protect himself a bit and hide behind them.