I don’t think those logically follow from each other, although I agree some people go that route. As evidence, I would offer
Kriegspiel, which was a war simulation used for training real officers by the Prussian Army very successfully. It is most definitely a simulation with no need to consider gameplay / enjoyment or story yet it was mostly operated by the referees judgement based on experience. It did not have a whole stack of specific rules or procedures for different kinds of activities an army might undertake. Hence simulation does not need to mean lots of rules.
A key feature of free kriegsspiel is - as your post says - the expertise of the referee. The referee makes decisions about what happens, based on their knowledge of how things would actually work out in a real war. This means that,
for the referee, the "game" is not a simulation. The referee is not simulating anything - they are making decisions by applying their knowledge.
I don't judge kriegsspiel, but I do sometimes judge moots, and they are similar in this respect: for the mooters, the situation is one of simulation; but for the moot judge, it is not a simulation. It is a deployment of expertise.
Sometimes mooters can who should win don't, because the judge's expertise is not perfect; and so the mooters who make the better argument don't have that recognised by the judge. I assume that the same thing sometimes happens in free kriegsspiel - that the referee makes a wrong call, and so a trainee officer whose forces should have succeeded in their manoeuvre, loses.
Underlying all of this - that the judge/referee can exercise expertise; that the "players" can reason about the imagined situation; that sometimes the judge/referee can get it wrong - is that there is an objective standard of correctness, namely, how things would
really unfold (in a battle) or what would
really be a good argument (in a moot).
And there is a through-line of Kriegspiel > Braunstein > Original D&D so I would consider that relevant to the topic of RPGs.
A difference between RPGing and free kriegsspiel is that there is no asymmetry of expertise. At least by default, the GM is no more expert in things like
how hard it is to climb up a statue or
how hard it is to pry a gem from the eye socket of a statue than any of the players.
In some approaches to RPGing - eg classic D&D - the GM has secret information, like the map and its key. This gives the GM a special role to play in dispensing information. But not more generally in the resolution of declared actions.