121 or 135, the captain, designated on the release, is the one that logs PIC. There is more than one subpart in 61.51: (e) (2) An airline transport pilot may log as pilot-in-command time all of the flight time while acting as pilot-in-command of an operation requiring an airline transport pilot certificate.
The captain on the release, check airman or not, is the PIC and logs PIC. If the captain losses qualification and a check airman is required to provide a line check, than the check airman will find his name on the release, because he, the check airman, has to be qualified to be captain, so he’s the one designated at captain. The check airman will probably be sitting on the right seat at the time. The PIC doesn’t even have to be required to sit in the left seat!
121.545 doesn’t reference anything about logging time, only who is allowed to manipulate flight controls. Manipulating flight controls doesn’t having any bearing on logging time under 121, and probably 135. I don’t fly 135. However, part 61 is the guidance for logging of time.