Conniew,
It's one of those "rules" that is intended to keep line employees from exercising personal judgment, avoid criticisms that one customer was treated in a preferred fashion over another with equal ownership rights, and keep auditors happy. However, no I would definitely not say that making the check payable only to "Varina" is wrong, it is just not what I would recommend.
In your example, I would make the check payable to the "Betty Jones Living Trust" and give it to Robert Jones. If its ultimate destination is the "Billy Jones Living Trust" I would suggest that Robert Jones endorse the check,
"Pay to the Order of the Billy Jones Living Trust,
Betty Jones Living Trust, Robert Jones, Trustee.",
Now, both the bank and Robert Jones have a clear paper trail regarding what he did with the money. (The trustee of the Billy Jones trust would still have to endorse the item.)
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.