If you have a witness that will give a statement, yes. If he does file charges against you, get a public defender and tie it up in court, but DO NOT pay him a settlement. Just drag it out and make it cost him as much money as possible.
If you need to buy time, ask for a continuation while you try to locate the fictional "witness" if you don't have one. Do a public records search of the scumbag and use that against him as well.
This guy doesn't want to go to court and risk pissing off a judge over something petty like this.