An affidavit of death and heirship is a weak claim to title. In Oklahoma it must be on file 10 years before it "vests" title. Sometimes a company is willing to enter a lease based upon such an affidavit. However, when it comes time to pay royalties they want a probate completed.
Fortunately, many cases qualify for a "Summary Probate" or "Ancillary Probate" which can resolve an estate in 30-75 days.