Was Arsene Right?

Quoted at Soccernet.com (here):

"Imagine the worst situation - we lose Fabregas and Nasri. You cannot convince people you are ambitious after that," he told reporters on the club's Malaysian tour.

"You cannot pretend you are a big club. A big club holds onto its big players and gives a message out to all the other big clubs that they just cannot come in and take [players] away from you. We worked very hard with these players for years to develop them and now it's time for us to keep them together."

That was a month or so ago. Nasri and Fabregas are now gone. Is Arsenal still a "big" and "ambitious" club?