Ann - You're correct that FBME and it's former name are not on the SDN List. However, I don't believe FinCEN's Final Rule states that OFAC screening is sufficient. I pulled this from the Final Rule:
"A covered financial institution is also required to take reasonable steps to identify any indirect use of its correspondent accounts by FBME, to the extent that such indirect use can be determined from transactional records maintained by the covered financial institution in the normal course of business. Covered financial institutions are expected to apply an appropriate screening mechanism to be able to identify a funds transfer order that on its face lists FBME as the financial institution of the originator or beneficiary, or otherwise references FBME. An appropriate screening mechanism could be the mechanism used by a covered financial institution to comply with various legal requirements, such as the commercially available software programs used to comply with the economic sanctions programs administered by the Office of Foreign Assets Control (OFAC)."
I read this as FinCEN using OFAC screening as an example of a way to detect activity with FBME. However, OFAC screening would not be sufficient alone, as FBME is not a sanctioned party (By OFAC).
"100 victories in 100 battles isnt the most skillful. Subduing the other's military w/o battle is the most skillful." Sun-Tzu