Remember, ratings go on your certificate, endorsements go in your logbook. Are you "rated" for an aircraft? Look on your pilot's certificate, and see if you meet all the requirements (category, class, and type if required). If the answer = "yes", then you are rated for the aircraft.
What does that mean? It means you meet the requirements of 61.51(e)(1)(i) to LOG PIC time when you are the sole manipulator of the controls. 61.51(e)(1) says nothing about endorsements being required to log PIC time.
Can you ACT as PIC, with regard to endorsements? This is where 61.31 comes in. If you are missing any of the required endorsements for the aircraft in question, then even though you might be legal to LOG PIC time, you cannot ACT as PIC. In this case, you must have another pilot on board who CAN act as PIC.
Here are the appropriate references from the regs, along with a legal interpretation from the AFS board.
61.31 Type rating requirements, additional training, and authorization requirements.
(g) Additional training required for operating pressurized aircraft capable of operating at high altitudes.
(1) Except as provided in paragraph (g)(3) of this section, no person may act as pilot in command of a pressurized aircraft (an aircraft that has a service ceiling or maximum operating altitude, whichever is lower, above 25,000 feet MSL), unless that person has received and logged ground training from an authorized instructor and obtained an endorsement in the person's logbook or training record from an authorized instructor who certifies the person has satisfactorily accomplished the ground training.
(Note, the above refers to ACTing as PIC and also references an entry in the LOGBOOK, not your certificate. Emphasis in reference is mine)
61.51 Pilot logbooks.
(e) Logging pilot-in-command flight time. (1) A recreational, private, or commercial pilot may log pilot-in- command time only for that flight time during which that person --
(i) Is the sole manipulator of the controls of an aircraft for which
the pilot is rated;
(Note, rated, not endorsed. Again, emphasis in reference is mine.)
Finally, here is the interpretation from the FAA legal eagle.
"14 CFR section 61.51(e) governs the logging of pilot-in-command time. This section provides, in pertinent part, that a private pilot may log pilot-in-command time for that flight time during which that person is the sole manipulator of the controls of an aircraft for which the pilot is rated. (Emphasis added)
The term "rated," as used under 14 CFR section 61.51(e), refers to the pilot holding the appropriate aircraft ratings (category, class, and type, if a type rating is required). These ratings are listed under 14 CFR section 61.5 and are placed on the pilot certificate.
Therefore, based on the scenario given to Mr. Lynch, a private pilot may log pilot-in-command time, in a complex or high performance airplane, for those portions of the flight when he or she is the sole manipulator of the controls because the aircraft being operated is single-engine land and the private pilot holds a single-engine land rating. Note, while the private pilot may log this time as pilot-in-command time in accordance with 14 CFR section 61.51(e), he or she may not act as the pilot in command unless he or she has the appropriate endorsement as required under 14 CFR section 61.31.
14 CFR section 61.31 requires a person to have an endorsement from an authorized instructor before he or she may act as pilot in command of certain aircraft (a complex airplane, a high performance airplane, a pressurized airplane capable of operating at high altitudes, or a tailwheel airplane). These endorsements are not required to log pilot-in-command time under 14 CFR section 61.51(e).
As you stated in your letter, there is a distinction between acting as pilot in command and logging pilot-in-command time. In order to act as pilot in command, the pilot who has final authority and responsibility for the operation and safety of the flight, a person must be properly rated in the aircraft and be properly rated and authorized to conduct the flight. In order to log pilot-in-command time, a person who is the sole manipulator of the controls only needs to be properly rated in the aircraft."