I wouldn't even give them the password to accounts I have on their systems, they should be able to access it themselves if the requester really has permission to view that data. The only exception I would make is to encrypted hard drives that they gave to me, but I would just de-crypt before ever giving them my password.
It's like if any company asked you for this info - I would ask for access to the CEO's email - or the financial drive and tell them that in order to work there, you'll need to perform an audit of their ethics and finances to ensure your not engaging in a relationship with a criminal organization.
