Removal of the collection from your credit report does not require any proofs or involvment of the creditor, PayPal, or the debt collector.
If you follow the indentity theft provisions set forth in FCRA 605B, the CRA must block any information pertaining to the asserted identity theft from your credit report.
The essential part of the FCRA 605B identity theft process is the placing of your assertion into a police report, which is acceptable to then block the information from your credit report.