Restricted-site.com gets the signed response from the broker, not the bank. In your situation there's not any need for "everyoneisover18.com" to defer to a real bank for a faked response as it signs things itself.
But restricted-site.com doesn't trust everyoneisover18.com's key, it only trusts realbroker.com's key, so the response isn't accepted. If it is found to trust fake brokers like that it gets in trouble with the law.
That's why everyoneisover18.com forwards the request to my bank or my broker and gets my signature on the behalf of literally anyone. I may charge them $5 for this service.