I feel like I'm missing something.
If someone breaks into my home and steals my TV, then sells it to a 3rd party and the police track it down, I get my TV back, as long as I can prove it was my TV. Offering my receipt that shows the serial number#, for example, would prove pretty definitively that this was mine, and that plus the police report and the photos of my broken front door and the missing TV would leave little room for doubt. It's that 3rd party that's screwed, not me.
Similarly, if someone tries to claim my home, or manages to get someone else to buy it by claiming they are the owners, I just need to prove it's my house. The fact that I have lived here, received mail here, paid multiple utility bills with this address, registered to vote here, have neighbors who will report me living here, and 2 RE agents who would say they were part of the transaction of me buying it, have mortgage records up until it was paid off, have contractor receipts for work performed, paid state taxes from this address, paid property taxes here, and probably many other things, would create a pretty compelling case in a he-said, she-said argument about who owns the house. The other party would have... none or almost none of those things.
It would be stressful and a PITA, but this is about 87 turtles deep on things I'm going to worry about, and on the very off chance it happens, I think there is almost no chance it doesn't eventually settle in my favor.