Arsene may not directly be on some crusade to prove everybody wrong but he sure has hell sits on funds. We sold Kolo & Ade the other year and Arsene & the board specifically said that all the funds from those sales were available to reinvest in the team, Arsene didn't buy anybody.
Arsene sets a very rigid criteria when it comes to buying players, he seems to set his valuations and if those aren't met then he won't buy. All this finding the "right" player stuff he comes out with pretty much backs this up. He would rather not buy and make do with what he has than go that extra mile and spend the extra when necessary.