First of all:
You started the thread on the premise that you are always required to file an alternate, and used the regulation regarding fuel to back this assertion. This is incorrect. The regulation you quoted, 14 CFR 91.167, regards fuel, and fuel requirements relative to your destination and alternate. It does not dictate a requirement to file an alternate airport.
91.167(b) exempts you not from filing an alternate, but from the fuel reqirements attached to an alternate. A subtle distinction...but in neither (a) nor (b) is the requirement to cite an alternate founded. Those are fuel requirements. 169(a)(2) sets the requirement for an alternate.
Back on point...the regulations under which you flew in the army are of course, irrelevant. How about the following quote from FAA Handbook FAA-H-8261-1, Instrument Proceedures Handbook (IPH), Chapter 2 (Takeoffs and Departures), under IFR Alternate Minimums:
You already supplied the following from AIM 1-1-19:
In addition to the guidance given from the AIM previously, 1-1-19 also includes the following statement regarding specific equipment meeting a specific TSO requirement:
Therein lies the crux of the answer to your question. Equipment certified under Technical Standard Order TSO C129, was certified with the intent of supplementing other onboard equipment. If your equipment meets only TSO Standard C129, then it was designed to meet a standard that intended for it to back up other forms of navigation...not be the only form of navigation. Accordingly, it's an equipment restriction, rather than a regulatory restriction that bars you from operating to an alternate soley with the GPS approach. Your equipment isn't certified for it.
If you're operating with equipment that meets a higher order of TSO, this restriction doesn't apply. If you use your equipment for a purpose other than that which it was intended, you're violating the airworthiness and operational standards of the equipment, and thereby unable to meet the requirements of the approach in the first place. If your equipment is used other than it's intended or certified purpose, your equipment is not airworthy...airworthy meaning both safe for the intended operation, and meeting it's type certification or standard certification...if it's use is outside that certification, then it's not airworthy for the operation intended, and therefore illegal. As a side note, that sets you up for additional violations.
WAAS certified equipment does not require other forms of navigation appropriate to the route flown, and is stand alone. Again, we read:
FAA-H-8083-15, Instrument Flying Handbook, Chapter 7, states:
The same chapter also states:
Advisory Circular AC 120-130A, Airworthiness Approval of Navigation or Flight Management Systems Integrating Multiple Navigation Sensors, Part 10, Operational Considerations, subpart C, Alternate Airports:
The bottom line is that one could go on and on with references, but as A Squared noted, you have the AIM reference, and that ought to be enough. The references in the AIM, while not regulatory of their own accord, are a compilation of numerous other sources, and it is an authoritative publication, as well as a Standards publication. You may also be able to tell that it saves you a LOT of legwork by bringing a lot of information to one central source.
As a professional pilot, you are expected to know, understand, and abide by all practices provided in the AIM...even if you haven't read it elsewhere, first. Regardless of the type of flying you do, it's a pretty darn good idea, anyway.
As an aside, consider the purpose of your alternate. It's your backup in case your planned efforts fail. It's where you're going to go that's your golden parachute in case you can't get in to your destination, for whatever reason. You're not required to have more than your minimum reserve fuel on arrival at the alternate. It's not the time to be engaging in guesswork, flying down to minimums with a possibility of not making it in, etc. The intent of the requirements to have backup means, including a viable nav means other than minimum standard TSO'd equipment and unmonitored navaids, is that when you get to that alternate you have something reliable and known to get you down. You're down to your backup options, and the purpose of these requirements is that these need to work.
If the navaid is unmonitored, you don't have assurances. If you're using equipment cited by the previous C129/129A TSO...ample possibilities still exist on arrival at the alternate that you may not be able to land, that using it as an alternate defies the logic and intent of the alternate in the first place. Therefore, safety and wisdom dictate that you use an airport that's appropriate to the purpose; you have a safe haven when you're down to your last legal gas and your last option...a sure bet. That's an alternate. Anything else wouldn't be wise.