How can someone sue for personal injuries when they did it pretty much themself and not on my property?

Your question leaves out a lot. Anyone can sue for anything pretty much. It is up to you to defend the allegations. Broadly speaking, you will want to show that you have no liability for any injuries the person sustained and also be ready to argue about the fair measure of damages if the plaintiff does establish liability. Attorneys are trained in evaluating cases and doing research to determine if there are any defenses and also how to bring in and keep out evidence. You should probably at least speak to an attorney about your case if you are not 100% sure if your position is legally and factually correct.