Agreed. If you don't otherwise, your bank should require a written partnership agreement as well. If this was "planned" by an attorney who mentioned partnerships or other business entities in the trust and then mentioned the trusts in the partnership agreement, it's a pretty sophisticated enterprise.
If, on the other hand, it's just something that some guys slapped together, the fact that they can do it doesn't mean you must open an account for them.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.