Just to play devil's advocate for a second, but as a pilot (even a commercial pilot about to be instructed by ATC) are you not still expected to look up conditions in the area of your flight? I would expect NOTAMs to be a part of that check of the conditions. If you know of the restrictions and ATC instructs you into that area, a quick confirm request about the NOTAM conflict does not seem out of place.
Yes & no, definitely more no for practical reasons. Let me explain;
ATC are ultimately expected to know about restrictions and keep traffic away from them.
NOTAM's are a notorious pain point for nearly all pilots. Modern EFB's make that easier, but in the 121 world - the ops folks handle your routing and plan for that stuff - as a pilot you "trust but verify", and most skim through the all the things (routing, fuels, weather, pax/cargo, notams, SIDS/STARS etc) to make sure that the flight is doable, it's doable safely, and it's "legal".
What you're expecting is a pilot to have a read a NOTAM, memorised all the latitude / longitude co-ordinates that are in the NOTAM for the "grid" that's off limits, and the associated altitudes, know exactly where that is in relation to where they are, and then be able to ask ATC about it a few hours into their flight, when the instruction could be as benign as "Delta 100, turn right heading 040".
Chances are the original routing for the flight kept them safely out of the TFR, but the ATC instruction for whatever sent them through it, even briefly. That instruction could've been for any number of reasons, from weather to traffic, to sequencing to even sidestepping a different restriction of some kind.
Here's a NOTAM for a Starship launch (I don't know if it was for this one specifically, I don't want to use my limited brain cells right now):
To underscore your point, the original flight plan almost certainly did not transit that region. So the pilot likely wouldn’t have even been aware that there’s a TFR somewhere vaguely adjacent to their intended path.
ATC issues minor deviations all the time and for a plethora of reasons as you mentioned. And those instructions are expected to be followed promptly, not “after I’ve spent a half hour re-reviewing hundreds of possible NOTAMs along the new course”.
Sure, of course if ATC tells them to land on a runway that is clearly occupied they have a responsibility to notice this and override.
In this case, they were directed into an area that was not occupied by an authority that controls the region's airspace. They could have asked ATC about it but ATC has control over the airspace.
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.
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.