And it wasn't just "one play" that was the reason the Pats weren't going to match the Philly offer (which was huge). Assante was horrible in run support and had a tendency to take chances on plays. This resulted in a lot of picks, but it also resulted in a lot of big plays for the offense. He also was better suited to play zone and wasn't an effective man to man player.
Now this isn't to say he wasn't, and still isn't, a very good CB, but not good enough for the Pats to give him the kind of money he was looking for. BTW- its not like they hated him or wanted him to walk. IIRC, the Pats made him a very substantial offer. Philly just offered a lot more, and we all know about Samuel's tattoo.