Thanks for all the great answers.
Ipse Dixit.
https://en.wikipedia.org/wiki/Ipse_dixit
It's a sort of appeal to a presupposed intrinsic authority of a statement.
Ipse Dixit seems to cover it well.
jp1692 It’s kind of a combination of “puffing” (in the legal sense), the common sense fallacy, making unfounded assertions and begging the question.
It seems these "weasel words" help lend support to a whole range of rhetorical fallacies. They work as a form of "appeal to authority." If the Watchtower/GB say something is clearly the case, then it must be, since they are the authority that know, regardless of whether or not any facts back up the statement.
They can be a subtle red herring, as the "evidently" statement hopes to prevent the reader examining that these is in fact evidence.
Interesting too that the legal profession and hypnotists recognise the power of using weasel words in a sentence.