Statute of frauds my friend. No paper, no contract.
The statute of frauds only protects the parties to the contract. In other words, if the guy who really “owned” the mortgage came forward and argued that the assignee did not, then the statute of frauds might protect him if there were a statute of frauds. It does not protect a third party, in this case the mortgagor who is not a party to the assignment anyway.
Besides which, there really is no statute of frauds for this particular issue, at least in most states.