There is nothing which specifically requires an instructor to occupy a control station, and in fact it is common in some circumstances for pilots to log PIC while not at a control station (long-haul airline CA, 141 Chief Pilot doing instructor check, etc)

But in aviation the legal right answer is not just what you read verbatim in the regs...it is a combination of (very poorly written) regs, FAA legal opinions, and case history from the NTSB.

In the case of a part 61 CFI, I'd bet the FAA would not accept that PIC time on an 8710.

Employers often have different, more stringent, requirements than the FAA...no employer would accept that flight time either.