it's easy to find a transaction with more than 10 BTC and claim the wallet as yours..
The signed message at the top of the first post verifies: OP really did own the bitcoins in 1EENuimoixhyn6k67UgeYo2mFFhRfEYots . You can check for yourself with Electrum: Tools -> Sign/Verify message.
However, it could be a lie if OP owned the address they went to as well, and there's no way they can prove they don't.