That story sounds plausible. Wenger doesn't spend a lot of time on the van Persie departure in his book. Just says it was feasible because the Ferguson relationship had thawed by then, but it was sad to lose all his best players to more monied clubs. He says after RvP left United, he asked to come back, but the only reason Wenger gives for rejecting the request was that we had moved on to younger players by then.
We lost far too many peak age, high quality players during that era. I'm disinclined to look at a parade of high quality players leaving and think every single one of them worms and bitches. That to me highlights a systemic problem. We should've been keeping van Persie, Fabregas, Nasri and all the other quality players we lost. Instead we kept guys like Walcott far too long. It feels good cursing out a fleeing rat, but we miss the underlying problems.