The two players don't connect to each other. They connect independently to the server. Your IP isn't shared with the opponent. There is no possible way he could affect your connection without taking over the chess.com server. And if he could do that, why would he waste his time stealing a few rating points when he could be stealing all the credit card info that paid members use to pay for their accounts?
Your suspicions are just paranoia.
I noticed that sometimes when I'm winning handily my connection will suddenly drop even though my internet is fine, and I'm starting to wonder if certain players have figured out how to game the connection stuff. I definitely didn't actually drop my connection and it's happened 4 or 5 times. I have to open it up on my phone and enter the game id as fast as possible to not lose time and it can end up causing me to lose in tight games where time is getting low. It really sucks when you lose a game because the website claims you dropped your connection when you didn't, especially when you're playing a really good game against a higher rated opponent.