Henry is on the right track here. When the puzzle says
you get to ask one yes-or-no question and get a response from one person.
you, if you were like me, probably read it as
you get to ask one yes-or-no question to one person and get an answer
As Henry realized, you get to ask the one question to the whole room (or alternatively, ask it multiple times until you get one yes-or-no response).
De-obfuscating the previous hint, two MDs = two doctors = pair of docs = paradox
No assumption needs to be made about whether the 99 truth-tellers can determine whether any other person is a liar or truth-teller.