SoCal,
I agree with part of your answer though I still don't think it is as clear cut as it should be. I agree that a strict parsing of the language seems to limit IGI activities to knowledge areas, 61.215(c)2 does not explicitly say what ground training for an IPC includes. Unlike the other two, it does not specifically impose limits but simply uses the unfortunatly vague word, "training". After reading the language below from the FAA, see if their use of the terms "Ground Instructor or Flight instructor" when discussing certifying simulator time doesn't seem to imply something different. The language below is not just random FAA verbage, it is from the official Federal register entry that actually officially unveiled the new Part 61. While not part of the regulation, it is part of the official clarifying language.
As for not needing an instructor present, 61.51(g)4 seems very specific:
(4) A person can use time in a flight simulator, flight training device, or aviation training device for acquiring instrument aeronautical experience for a pilot certificate, rating, or instrument recency experience, provided an authorized instructor is present to observe that time and signs the person's logbook or training record to verify the time and the content of the training session.
But the following official text from the Federal Register clearly states the opposite!
Therefore, a person who is instrument current or is within the second 6-calendar month period (See§ 61.57(d) for currency) need not have a flight instructor or ground instructor present when accomplishing the approaches, holding, and course intercepting/tracking tasks of § 61.57(c)(1)(i), (ii), and (iii) in an approved flight training device or flight simulator.
(See
Federal Register | Pilot, Flight Instructor, and Pilot School Certification
)