Someone says I hit them but I didn't

Latency (the time it takes for data to go from your pc to someone else's pc) and thus desync (your car being in a different position or doing something slightly different than what you're really doing in someone else's view) is an annoying, but constant reality of online play. Even at low pings, your exact position on someone else's screen isn't going to be identical to what you see and this can lead to issues when you're racing closely with other drivers. This is why I recommend giving people more space than you think they need and avoiding bumping into players as much as possible, since a light rub on your screen might end up being a full-on shunt on theirs. You can also try and have consistent, clean inputs - ie turning the same amount through a whole turn and avoiding sudden shifts or corrections - as this will mean that the game's assumption on where you're going to end up is going to be as close as possible to where you really are.

Sometimes, even despite your best efforts, in a close race lag will lead to someone getting knocked out. Sometimes, lag won't be an issue and instead someone will just make a mistake and slide into the nearest wall. As you play the game more and get more knowledgable on how cars look and move when losing control, you can start to make the judgement call between whether someone getting sideways beside you is because your car knocked them on their screen or because they just made a bad turn or hit an obnoxious bump in the road. In general, if you're not sure if you knocked someone or not, let them catch up! Races aren't so serious that you need to risk accidentally screwing over other drivers to get that extra place or two, and the more you race the easier it will be for you to say 'no, that guy just made a mistake' and drive on to victory.