no way to verify it isn't beyond "trust me bro" and I don't trust them

If the verification service is structured like oauth, then the request could be passed through the browser as signed plaintext. You could verify that the requesting site is only passing a minimum age request to the service. That would be as straightforward as viewing the interaction in your browser's debug tooling.

If you say that you don't trust the signature, and that it could be used to smuggle identifying information across, there's a couple of ways to deal with that: open source and audited provider governed by legislation; information theory that would show personally identifying information wouldn't fit into a field of that size; and "personal auditing" where you can try throwing data at the service to see if you can trick it into accepting invalid input (that really goes with the previous point, because the only field you can usefully vary is the signature).