As I posted a month go, I would have expected Belichick to give Cassel and his agent permission to try to work out a long-term deal with other teams and have the teams come to the patriots with their offer to the patriots. Cassel's agent and the other teams would know what the patriots were loking for in compensation, but the final decision would be the patriots. Cassel's agent would indicate which teams had presented acceptable offers to Cassel. In this way, as I have continuously said, Cassel would have maximized the value to the team, although perhaps not to himself. If he has confidence in himself, he could and did take the $14.6M, buy an insurance policy, and can consider a long-term deal at a later time, perhaps after the season.
Apparently, the team's alternative was to not have Cassel as part of the decision-making process, other than to ask if for input that was of little use in making the deal. With Cassel not part of the process, a team would need to make a deal for Cassel with no long-term contract in place, thus limiting the teams in play plus limiting the compensation to the patriots.
ALTERNATIVES
1) The team didn't consider the above (not very likely).
2) The team presented the idea to Cassel's team and they didn't do anything with it, either refusing or not finding an acceptable deal.
3) The team decided very early with Pioli and decided not to try to get more. This could have been because Pioli made an early offer that had a time limit and the patriots accepted.
I find both options 2 and 3 to be very possible. I lean toward 3.