Well, it obviously is a balance between what the manager wants and what the board can afford to get. The key is to negotiate and find this balance. It's very easy to blame someone, say the board gives O'Neill a budget of 200k per week for the transfer window and he buys Beye on wages that are high but within the set budget - then who's fault is it? I say both are wrong.
Every football club has a team that should be both financially aware and with enough footballing knowledge, so that they would make the decisions in the best interest of the club. Now, obviously they'll make mistakes, but overall they should be steering the club forward. This hasn't been happening at Villa for a while now and with quite a few different managers. Also, as much as I agree that managers don't want to be controlled by the board, it is very naive to think that the manager himself does all of the transfer business, from the fee negotiating to the contract detials.
As for Chelsea, they have been successful because Abramovich has more money than common sense, but I'd argue they would have been even more successful if he had let Mourinho do his thing and hadn't fired him.