It's exactly one month since I asked the same question
and no one has stepped into the breach since. So, this response is purely from me.
The bank is on notice that the attorney with an IOLTA account is a "professional service provider" as discussed in the Examination Manual; i.e. it knows that the attorney is a "gatekeeper" and the money in this account does not belong to him or the law firm. In FIN 1989-R005
FinCEN made it clear that if a reportable cash deposit is made to the IOLTA account, the bank is required to identify the client on the CTR. Following the same logic, I would say the bank is definitely required to identify the client as the originator of the wire transfer.
As your employees are probably more afraid of asking lawyers questions than they are clients in general, I suggest you submit your question to the Helpline. I will do the same and we can compare notes.