Scott, when you write "taking any FAA-prohibited medication" do you mean medicines on the "Do not issue" list or do you mean medications on the "Do not fly" list? Your term, "FAA-prohibited" is not used in the link you provided.
Here is the applicable language regarding pilots who do not require an FAA medical certificate (I provided the link previously):
"b. Operations that do not require a medical certificate.
For operations provided for in 61.23(b) of this part, a person shall not act as pilot in command, or in any other capacity as a required pilot flight crewmember, while that person knows or has reason to know of any medical condition that would make the person unable to operate the aircraft in a safe manner.
c. Operations requiring a medical certificate or a U.S. driver's license.
For operations provided for in 61.23(c), a person must meet the provisions of Paragraph (a) of this section if that person holds a valid medical certificate issued under part 67 of this chapter and does not hold a current and valid U.S. driver's license Paragraph (b) of this section if that person holds a current and valid U.S. driver's license."
So, the critical issue is what is meant by, "knows or has reason to know of any medical condition that would make the person unable to operate the aircraft in a safe manner". I believe that requirement is not the same as taking a medication that would prevent the issuance of a Class 3 or other medical certificate. Do you have a basis in terms of FAA actions for your opinion?
Under the requirement listed in the regs, the process changes from a checklist-based system (i.e., do you take THIS medication, do you have THIS illness?) to a performance-based system (i.e., are you able to operate the aircraft in a safe manner?).