Hi mokkyukkyu,
The claim in question is indeed a hypothesis, because it attempts to provide a cause for the observed effect: given the proliferation of monarchist arguments, some people believed that mechanism and democracy don't mesh well. This is a theory, or a hypothesis, that attributes a particular explanation to an observed phenomenon. And yes, indeed, this hypothesis - like many others - is a matter of belief. Beliefs can be construed as evidence. There is nothing wrong with that
The argument challenges this hypothesis (or explanation) by providing an alternative one: perhaps the principles of mechanism actually support democracy, and the arguments multiplied because none of them worked.
Hope this helps!
Thanks,