See, these "proof of payments" are fucked. Nowadays people are not even using signed messages anymore, but blockchain transactions which could be theirs or could belong to some random person. Thus a person could commit fraud by producing an arbitrary transaction on a block explorer as a "proof of payment".
This "proof of payment" is only valid between buyer and seller, and meaningless to everyone else. There is no way (currently) to prove that you actually sent Bitcoins somewhere.
My goal was to verify if the OP really sent BTC from the input address of the transaction he linked in the OP. People can take random ID from blockchain and claim that it's their transaction. But anyway, we already know now what happened. Thanks to khaled0111.