Why did they order the spygate tapes to be destroyed? They wanted to limit the damage. If they truly had their way, they would sweep this entire thing under the rug. The thing that's working against them is that the interests of one team doesn't usually overcome that of every other team.
The bottom line is that this team has a history of cheating as the day is long, both on issues that are widely known and some that aren't. For example some Patriots employees were involved in things like stealing playbooks from hotel rooms, bugging locker rooms, etc..