Papers are proof of ownership when the person cannot provide a bill of sale or any proof they bought the horse, the owner has reported the horse stolen (which should have been done if it hasn't), and you can prove the horse is the same one as on the papers. If you had papers on a horse and it was taken from your pasture one night then as soon as that horse was found no matter how many times it had been sold so long as it can be identified as the same horse without question you still own it. The papers and lack of bill of sale from the owner on record of the papers along with a report it was stolen at the time proves ownership and theft. That's one of the major points of having registration papers. Proving a horse is yours.
This actually somewhat came up but on a more minor issue. I gave 2 horses to a friend and gave her the papers with filled out transfers. She never sent them in and the horses remained in my name the past 2 years. She loses the transfers. There is now no proof I gave the horses to her. I still hold the papers. She had them on leased land. Then she ended up going through a divorce and not paying as much attention to the horses while the land owner decided to claim them as his and give them to someone else. She had no proof of ownership and couldn't get them back. I instantly got them back. They were in my name. There was no record of bill of sale and they were obviously the horses on the papers. After they were moved without authorization I reported them stolen. The police took the papers, went to look at the horses, and under my authorization and with new transfers filled out gave the horses back to my friend. It's really not that difficult.... Papers, a report of the horse being stolen, and no bill of sale should be more than enough to prove ownership. The lease and proof of attempts to contact the lessee just seals the deal. There is no legal difficulty here. This is just a case of the authorities being lazy and not wanting to deal with it.