I'll post a quick response, but will try to consider your questions some more and might address things deeper after this weekend.
There are many ways to address that type of claim. There is some validity to it, there is also some deception, exaggeration, and impracticality.
Maybe it might be better to break down suffering into 2 layers:
1 - Direct physical pain, discomfort, injury, nervous system trauma, confusion, instinctual fears, brain imbalances
2 - psychological suffering, fear of pain, fear of feeling, fear of thoughts, inner critic, delusions, distortions, imagined dangers
'The work' can be useful to address 2nd level suffering, but not really practical for 1st level suffering..
An example: I just got stabbed, there is a knife in my body, I'm bleeding. If I'm still in a fight or altercation, I should defend myself, and seek physical safety from danger. Then I should seek medical care & attention to tend to my wounds so they can heal. Doing 'The Work', and asking the 4 questions at this time, is not very helpful, and would be a major distraction and the extra delay could cause me more harm.
Part of what I have observed with the way people actually practice 'The Work' is that they think of it in 'magical thinking' terms, instead of recognizing the limitations to this method (or any method), they self-blame, and too easily jump to a conclusion that they aren't doing 'The Work' hard enough, or doing it enough times, or they are doing it wrong, or need to get an expert to help them do it.
And Byron Katie and her authorized facilitators can propagate this type of dangerous 'magical thinking'. I recall seeing an authorized facilitator give a presentation, and it was totally obvious that she was simply reading a presentation but didn't really grasp & understand the actual material and process. I even personally saw Bryon Katie do a Friday night introductory presentation, and all she did was robotic type 4 step questions with a few participants from the audience.
It's nice that she was able to package self-inquiry into a 4 simple question process. You'd think that people could just take that and run with it themselves. But from what I've seen, people are just too confused, lazy, or unmotivated to regularly practice 'the work', and never ever get to a proficient level where it's a sort of natural or automatic way of thinking.
It's the same thing with meditation, you start with a regular structured formal practice. With practice it should become a habit. And with time, it should develop into an automatic state of being, you're mind is always in a state of meditation, inner calm and clarity. Meditation becomes the default state.