The short answer to your question is that there is no law or
requirement to use TSOA headsets in any aircraft by any crewmember,
under any operating rules, whether Part 91, 135 or 121, or under Part
25 or Part 43 or any other FAR.
This information was provided by Inspector Bures, the Aviation Safety
Inspector (Airworthiness- Avionics) of the FAA Flight Standards
District Office (FSDO) in San Antonio, Texas, with whom I spoke by
telephone.
The contact page for that FSDO is here:
http://www.faa.gov/fsdo/satfsdo/off_person.htm
He said that the FAA's TSO program with regard to headsets and
microphones is for the purpose of establishing a standard, or
benchmark for such equipment, but that the FAA has not mandated nor
regulated the use of such equipment.