While Im sure that Belechick watched the tapes of how the giants played the Rams and Im sure John Fox watched the tapes of how the Eagles played the Rams and Jim Johnson watched the tapes of how New Orleans played the Rams. All of these teams did play them differently. New York and Philly both used a two deep scheme similar to the one that worked so well for Tampa and New Orleans and blitzed the hell out of the Rams, or applied pressure by having Strahan line up over John St. Claire. New England didn't have the personnel to pull that off. Now they too relied on limiting yards after catch but they went about it more with a soft zone where they kept the receivers in front of them. So yeah they beat the crap out of them like the Giants did (in a losing effort) and the Eagles did (they lost too), but they went about it with a different scheme (I think they liked their results).
This reminds me a little bit of when Butch was coaching at U Miami. Granted, they were under probation sanctions from the NCAA for several years, and that was part of the problem. However, it was a very mediocre time for UM.