Answer:
This typically comes up when the trust in question is a grantor trust and the payee on the check is the grantor/trustee. Once the check is indorsed by the payee, it can be deposited to the trust account in such circumstances.
The reverse of that situation -- when the check is payable to the trust or the trustee and the requested deposit is to the account of the individual -- doesn't have such a facile solution. In those cases, it's preferable to deposit the check to an account of the trust to avoid any potential claims that the check was converted by the individual with the knowledge of the bank.