I think you should stick to Facebook's TOS (Terms of Service) in all your relationships, both in terms of not giving your password to others and obtaining other people's passwords:

You will not share your password (or in the case of developers, your secret key), let anyone else access your account, or do anything else that might jeopardize the security of your account.

It makes sense because it was really really weird of him to try this approach of giving you his password to prove his honesty since you should not be viewing his private content in the first place, for any reason.

So, still very weird.