Yeah I have to agree with the others. Mineral rights do not go back to land owner.
My personal experience is in North Dakota. These rights have been split any different way from Sunday, but the rightful heirs still have claim to them if they want to probate the wills involved in North Dakota. If they don't go through this process the royalties go to the state of North Dakota in this case.
Your cousin is maybe thinking he can get the Lease money which Oil companies seemingly are not as picky about proof of ownership. However when Royalties start coming in he will have a tougher time laying claim to them as the Oil Companies require proper proof of ownership.
Simple version get yourself a good Ohio mineral rights attorney. Do NOT shop on price. In North Dakota I can name one attorney to Run away from at a thousand miles a hour and can recommend another. I am a trustee with a trust that was set up to gather up these rights into a more salable product which we are now trying to disolve. This whole process has cost the beneficiaries many thousands in legal fees caused by the train wreck of the original attorney.
Get a Good Attorney. If you don't have a family attorney who can recomend one maybe John T can help.