Sounds like you are not talking about a personal trust (e.g. John and Jane Smith Family Trust). A trust like that comes into an existence when a trust document is written (outlining all the terms, such as beneficiaries, trustees, asset addition/management/disposition isntructions, etc.) and executed. In other words, if there is a trust, there is a trust document. What your institution requires to open a trust account, is a matter of company policy (including CIP requirements). We would never open a trust without getting documentation (usually the trust document itself) clearly stating who beneficiaries, trustess and successor trustees are and what authority they have been given to act on behalf of the trust.
But what you have on your hands may be something more like an "escrow" account. Again, due to our policy we would not open one of these because there are just too many unknowns: who can access the account, when, etc.
Opinions are my own.
"I was gratified to be able to answer promptly. I said I don't know." - Mark Twain