Good advice by suggesting him to find someone else to borrow his documents, I myself certainly do not lend documents to just anyone, only to people I trust, as I have said it is indeed quite risky but I do not forget to always consider it first because I myself do not want to experience problems with my personal data.
With what you do when a friend wants to borrow a document to verify and you do not lend it, that is the right action, because that way your documents will be safe, keep it. Maybe I myself will try to refuse my friend who borrows my documents later.
You are right because we must responsible our document and not giving easily because of a nice offers from our friends. True friend will not takes his closest friend and risk him by using his identity just to verify his account in gambling. He will understand the risk so he will not trying to force us to gives our identity to him and he will search for the other ways. You should try that because that is for your safety and stay away from the risk. I am sure you can explain that better to your friends that want to borrow your identity and they will understand your explanation.