Some banks will check the name of the incoming deposit and return it if that person is not on the account.
From a bankers perspective, why are they doing this? When the money goes into your account, it is your money. You own that account. If they are attempting to hide it because of some litigation, such as shielding it from a creditor, your own money may get tied up if the account is found and garnished or levied. If you give that person access to your account, you are giving them access to your money as well.
Is it worth that risk? Let them meet the minimum balance and open their own account for free or $6.95 a month.