Answer:
by Randy Carey:
Once the trust goes to an irrevocable status which is caused by the death of the grantors, it needs a separate EIN. What you accept as deposits into the account is a business decision.
Answer:
by Ken Golliher:
If you meet resistance, remove the SSN because you know it's wrong. Then, impose backup withholding because you do not have a properly certified TIN.
Hearts and minds will follow; i.e. they will get you an EIN. If they get mad at you and move the trust, then the next bank will require them to get the EIN.