You dont let guys like Peterson leave your team. You pay them, and thats that.
In the salary cap era you do if you want to succeed--for an example see the Patriots. The beauty to the NFL under the cap is the parity so that any team could be 3-5 years from a super bowl. The down side is the hard decision to let either (a) great players that have been on the team and are on the down side of their careers go or (b) great players go just because someone, cough Snyder cough, will try to buy a championship now and drive up the price of players. It's simple math, if you have $80 mil to spend and you give one guy an extra 5 it comes from somewhere. Obviously you try to keep your best players, but "at any price" has no place in today's NFL.