Kind of - but we need to look at Wenger's definition of 'the best he can'.
For the manager, its seems as though this phrase is qualified. He wants to do the 'best he can' while remaining financially conservative. Unless someone is denying him the funds, this qualification is in his gift to remove, so the situation is akin to a golfer choosing to compete with outdated clubs; or a Formula One boss deciding to race with last year's model. I don't buy that that is doing the best they can. In transfers at least it is clearly Wenger with the handbrake on. His choice ultimately. Its not a question of whether he cares, its a question of whether he is putting his team in the best position to try to win things, and he patently is not.