It’s more of a rule of thumb that is rooted in evidentialism. I’ve always viewed it as a shortcut to lead evidentialists away from wasting time on argumentation that is ultimately rooted in faith.

If you’re looking for examples of its application being sound when frequently applied to religion, watch some Atheist Experience; it comes up a lot on there.

Yes, one can assert that a principle is useful, but that is not the same as asserting a specific claim. The point being made is about buttressing claims with supporting reason and evidence, not that making an uncomplex statement can be casually thrown out.

A different expression of the same idea is the (relatively new, but still not as recent as the 20th century) Latin phrase “Quod gratis asceritur, gratis negatur” – loosely “That which can be easily asserted can be easily negated”. The criticism is again of the support for the specific claim being made.

The point that unifies these two statements is that it takes effort to produce a robust, defensible, truth claim. What the Latin describes as an “easy” assertion, Hitchens can be read to imply as being lazy i.e. that gathering evidence and clear reason takes time and energy.

As to this principle itself, I would have difficulty arguing that it is easy to produce a valid truth claim without at least some effort. Brandolini’s Law is an observation that it is easy to produce false or misleading information and difficult to refute the same. This is, again, just a distilled observation of a pattern, and the argument supporting it regresses to gathering as much bad information as possible, pointing at it, and saying:

“All of that wasn’t checked and because we now have to unlearn these falsehoods, it takes that effort as well as the effort of learning the truth to improve our knowledge from this point.”