I don't disagree with Ron on this that you are technically allowed to log this as PIC,
The trail of quote-backs is a bit vague, but if we're talking about the situation where you are acting as PIC while an appropriately rated friend whose medical is currently invalid flies the plane, then unless the friend is under the hood (in which case two pilots are required), you cannot log PIC time even though you are the PIC.
but I have seen the FAA issue a notice alleging that the pilot conducted flights as PIC with an expired medical based on his entries as PIC in his log book.
Unless there was no other appropriately rated and fully PIC-qualified pilot in the aircraft, I'd like to see that "notice."
This came up after he had a hard landing in his new LSA on his way back from purchasing it. The FAA looked at several flights he logged as PIC that he had made in his old non-LSA aircraft before he sold it during a period of time when his medical had expired. He told them he logged the PIC time as the sole manipulator of the controls, and that there was an appropriately rated pilot on each of the flights as a "safety pilot." They asked him to identify the "safety pilots," and then interviewed the individuals that he could identify as flying with him (although his memory was foggy, and he didn't have the names of the pilots written down). When they couldn't confirm whether they were acting as PIC, or that they were even in the plane on those flights, the FAA issued the notice that they intended to suspend his license for 120 days for all of the alleged violations.
There have been cases where the FAA has gone after the person whom the unqualified pilot claimed was acting as PIC, but the alleged PIC disputed that and was able to show by a preponderance of the evidence that s/he had no idea the unqualified pilot was unqualified or that the unqualified pilot was relying on him/her to act as PIC. That's rather a different situation than we are discussing. However, it does point out that even though the regulations do not require the unqualified pilot to name the person acting as PIC in his/her logbook, it might be a real good idea to record that name anyway. It's also a good example of why whenever there are two rated pilots in the plane, it's a real good idea to discuss and decide before engine start who's actually the PIC for the flight, and what duties/responsibilities (if any) the second pilot will have.
Ultimately, the claims based on the old flights were dropped in negotiation with the FAA staff counsel. The pilot ultimately accepted a 30 suspension due to the undisputable fact that his BFR at the time of the accident flight was not properly logged and signed by the CFI. In fact, there was no entry in his log book at all, although he claimed that he had had a BFR.
Sometimes the FAA will settle like that. Sometimes they won't.
It may be that they dropped the old flight claims due to the stale complaint rule,
Not likely. The 180-day clock doesn't start until the FAA discovers the violation (in this case, when they saw his logbook with no flight review endorsement in it), not when the violation actually occurred (i.e., when the flight without current flight review occurred).
or it may be that because they were getting an agreed suspension they didn't care if they let it go, and the pilot was cooperative with their investigation, and affirmatively took steps to go out and get a properly logged BFR after the accident.
That sounds like the FAA I know.
Again, I am not saying Ron is not correct, I am just saying that there may be a risk of FAA scrutiny if you do log PIC with an expired medical.
Only if, in the event the FAA becomes involved, you can't show by a preponderance of the evidence that someone else was acting as PIC at the time. The story as you tell it suggests that the pilot involved could not, largely because the other pilots denied they were acting as PIC for those flights. If you make a habit of discussing with anyone acting as PIC in this situation that they are acting as PIC, and you put their names in your logbook, the FAA will have a tough time proving they weren't the PIC for that flight.