Yes, actually, we do have some surviving forged claims. The
Registrum of Peter the Deacon in southern Italy is full of them. Monastic archives from areas like southern Italy and Mount Athos in Greece (which are our some of our best surviving medieval document collections) contain some very spurious property claims indeed. There are also famous, high-profile forgeries like the
Donation of Constantine. The Norman kingdom of Sicily was founded on the (completely fictional) basis that Roger II was restoring an ancient kingdom that had been conquered by the Arabs, whereas the island had of course belonged to the (still extant) Byzantine Empire. And so on.
You're right to say that medieval records weren't spreadsheets that you could hack into and edit. It was actually much easier than that. In a period when most people (in western Europe at least) were functionally illiterate, it was actually quite simple for a well-educated person to learn a little about the history of a place, look at some real documents issued by famous kings, bishops, and judges of the past, and then create a fake document. All you needed was a straightforward mock-up of a legal ruling that determined that a plot of land belonged to one of your ancestors, or to your monastery, or some such. In an age before textual criticism, it was really very difficult for people to figure out what was a genuine historical legal document or something that an educated person had mocked up for themselves.