Look, I'm sorry but that is not correct. The "privilages" are associated with the pilot certificate, not the medical. The thing that trips everyone up is that an FO really only needs a Second Class Medical, so the two get overly associated. Here's the FAR again:
61.23 (d) Duration of a medical certificate. (1) A first-class medical certificate expires at the end of the last day of—
(i) The sixth month after the month of the date of examination shown on the certificate for operations requiring an airline transport pilot certificate;
(ii) The 12th month after the month of the date of examination shown on the certificate for operations requiring a commercial pilot certificate or an air traffic control tower operator certificate......etc.
If you are working as an FO, that is an operation requiring a commercial pilot's certificate, and you are operating for the full 12 months on a First Class medical. If the guy has a first class medical, then 11 months later it is still a first class medical but is only current for operating under the PRIVILAGES of a commercial pilot's license (FO) or private pilot's license. It is still a first class medical, no exeptions, no modifiers.