Actually, Van Persie didn't agree personal terms with the rags until the 14th August, which was after an agreement had been made between the clubs.
Van Persie announced he wanted to leave in mid-July, but there was a number of potential suitors at the time and he hadn't a preference either way.
In this instance, Sanchez has long announced his intention to leave and is clear where he wants to go - City. This is, as it happens, how City do business, ie, get the player on board first to speed up the process. Further, I'd argue there's not the competition existent to snatch away Sanchez. Yes, Bayern are there, but if the player doesn't want to go to Germany he won't go and that's before the financial difficulties involved.