Well there's "centaur" chess where folks use the output of numerous engines as well as their own skill to craft a game. The games that result are of very high quality. That's legit, and you can play that here as long as the game is labeled as computer assisted. Some sites have given up trying to police computer use in correspondence chess, but certainly not this one.
As to why folks accuse each other of cheating, it's just ego. Well that, and the usual adolescent hormonal imbalance. 
Hello Everyone, I recently switched from chesscube and I love chess.com for the obvious reasons. Unfortunately a lot of people call other cheaters, at times I am acused of using computer assisted chess modules as well, which I find offensive as I would never say that to someone. I accept my loses and keep my ego on a leash. I can't understand why someone would cheat; our common goal is to get better at chess right? My rating is my instant performance outlook, and it seems that's the most important thing on one's profile. So my question was, if computer assisted chess even exists, and why do people use it? All I understand is that people are too ashamed to accept their defeats and it's a cheap couple of words to throw out there..
Thanks for any explainations.