[s1artibartfast]

If ATC put them straight into a Mountain, would it be correct to dutifully fly into it, or would that be an error on the pilot side?

My understanding is that Pilots are also required to review NOTAMs. There are tons of systems and operations with redundancy built in. An error in the primary does not negate an error in the backup. In fact, it is often the only way you learn of errors with the backup.

[stouset]

ATC instruction can be countermanded in the event of gross error or emergency.

That said, ATC instructions are to be followed promptly in the absence of such factors. You don’t get to wait and check hundreds of possible minor and irrelevant NOTAMs to find the before following through on their instruction, on the off chance they’ve completely screwed the pooch and are sending you through a TFR.