A preimage proves the secret behind a payment hash was released, so the HTLC for that hash settled against an invoice the receiving node signed. It doesn't prove who paid, it stops being secret once every hop on the route learns it, and with a custodial Lightning address it only shows the host's node was paid. The note walks through BOLT 11, 2, 4 and 12 (including BOLT-12 payer proofs) and what that means for honest tip-jar bookkeeping.