Thanks Omnicron, I did actually ask the seller of one in California who said there are lots of foreigners who own claims... it appears from the article you linked to that this isn't the case as we'd need to be US Citizens.
I strongly suggest people do not buy claims if they don't already have the experience of discovering a valuable mineral deposit, recording and staking that location and working their claim at a profit. Anything less and you couldn't possibly have the knowledge to judge the value of a claim for sale.
The law is clear that only US citizens (or those who have stated their intention to become one) can own claims. You can form a domestic corporation in one of our States and use that as a lawful way to own a claim.
There are many claims for sale that are invalid. There are many claims for sale that do not have any gold. There are many claims sellers who prey on the uninformed. It is a whole industry in our western goldfields. I know of several claims sellers who salt their claims and mislead the buyers into believing they are buying private property and can build homes and live on the claim. The world of claims selling is full of criminals and misinformation. We see this everyday in our work.
Many claims sellers will tell you whatever you want to hear to make the sale. The above seller is an example. The link offered earlier is incorrect also when they state that a single person can own a claim larger than 20 acres if they buy it from another person. That is a very misleading statement.
There is no enforcement authority to back you up if you are lied to or cheated when you buy a claim. There are no claims police and no authority checks claims to make sure they are valid. Anybody can make a bogus claim and sell it to the first gullible person who happens by. Under US and State laws it is up to the individual to do their own due diligence when locating or purchasing a claim.
Ask yourself - why would anyone sell a paying claim for less than the value of the gold they can mine from it? It's very inexpensive to keep a valid mineral claim so what is the incentive for the seller?
There are real producing claims for sale at times but without a very good knowledge of the business of gold claiming and mining there is no way to tell the authentic from the scam.
There are huge areas of paying ground still open to prospecting and claim in the United States. Plan on prospecting those areas and discovering a valuable mineral deposit. In the process you will learn the ropes and come to value and respect the work and knowledge involved in making a valid claim. Then you can think about buying a claim, I'll bet you won't though.