Oro: while you are correct, strictly speaking, about the requirements for filing a valid mining claim (varies widely by state), these requirements have never been 'inforced' (by whom?) in the last 100+ years (at least in NM, AZ or CO, where I've filed lots of them for other people and myself). As long as the claim's location has been described within the proper quarter section, the corners more or less properly erected with a copy of the location papers attached at one of the corners at the time of staking (varies by state) and the filing fees paid at the county courthouse and with the BLM, the claim is considered legal. No proof of mineral discovery is required. The claim remains valid as long as the yearly assessment requirements are met (now a yearly fee paid to hold the claim).
You are correct that a huge majority of claims filed within the past several generations have been speculative - most by the mega-corporations but also many by the small-time miners (now nearly extinct). While this is done to tie up all possible ground surrounding anticipated mineral deposits, these deposits remain speculative until they are mined, if ever (most never were). The only time legal issues arise concerning unpatented mining claims is when the operator decides to begin mining and he has to file operating plans, environmental impact statements, post bonds, and a number of other red tape items.
Cayce's son or anyone else had a legal right to file a mining claim or a group of claims as long as he was an American citizen, filed on ground open to mineral entry and not currently held by someone else and met the state's requirements mentioned above. This used to happen all the time, but is becoming a rare occurance nowadays.