They didn't say things should be accepted without evidence. That's a laughably bad-faith reading. They proposed a different standard of evidence that they think is less infeasibly high while still not accepting nonsense. I don't totally agree but it's a reasonable direction to argue.

As for the examples, when they start with "swings over the years" they're clearly taking a long-term perspective, and not trying to claim that modern archaeology will "believe anything" (especially not when their more prominent claim is that modern archaeology believes too little).