Not necessarily. He can first transfer whatever amount is still in the address controlled by that key to another address and then publish the private key of the address that now has a balance of zero. What's the problem with that?

Because now the people behind satoshi-test.com have it and can claim to be satoshi.

It needs to be something like "Please sign `<challenge string> + your name`"

If someone spends the first block or any which is believed to be held by Satoshi would be noticed and the bitcoin market would panic. Satoshi is alive and spending their money!! Sell now!