He still had the advantage back then. I believe Belichick was still employing nefarious methods of stealing the opposing teams plays and such. The evidence shows as much. In fact, his record "pre-cheating" (which includes his first year in NE) is telling: 41-55. That is NOT a coincidence.
So what you're saying is, even though the "advantage" was taken away from him, he still had the advantage anyways?