I've always taken rebellions to be in-fighting between nobles on a massive scale. Meanwhile the government label of Anarchy is when there is no control whatsover, not even a contested rulership. Anything could happen during that. The peasants could form their own government for all we know IC.
Rebellion is, indeed, nobles fighting against each other.
However, when a rebellion succeeds without the ruler stepping down,
there is a period of anarchy. This is what allows the new ruler to change the government type.
And no, the peasants bloody well cannot form their own government. Any more than a message can be forged. Or a noble can die from an infiltrator attack.
Anarchy is not "no control whatsoever". It's a lack of a cohesive central government. The nobility are still broadly in control of the realm, there just isn't all the usual bureaucratic infrastructure to get things done.
Anyway, like I said, twice now,
the only possible way for any player to change government types in BattleMaster is to go through a period of anarchy. So objecting to anarchy as "an acceptable means" of changing a realm to a theocracy is really...not very sensible. Basically, by your logic, no realm on Dwilight should be allowed to voluntarily change their government.