But no, I don't debate your point. What I was addressing is what would motivate someone to promote something but at the same time deliberately reject it, as in the overweight doctor example. It's hard to think of an example that fits critical thinking.
Skill, and boredom at working through "classroom exercises," for one possibility.
I know of, for example, a few superlative mathematicians who are much better at teaching proofs then they are at actually producing or publishing them. When doing their own (research) mathematics, they rely very heavily on their own intuitions and guesses about what conjectures are likely to be fruitful and interesting. They are essentially lean, mean, conjecture-making machines. On the other hand, they often can't
prove their conjectures.
They make great collaborators. They'll come wandering into your office, saying "wouldn't it be interesting if [insert technobabble]?", without the faintest notion of how to prove it -- but then will happily co-write a paper with you once you figure out how to prove this interesting conjecture that you yourself wouldn't have been able to come up with. (For an example of this that you may have heard of, consider Len Adelman's contribution to the RSA algorithm. He was the cryptanalyst of the trio, and spent his days breaking the cyphers that R(ivest) and S(hamir) invented each night. When RS finally came up with one that A couldn't easily break, they published -- and thereby won the Turing Award.)
I've seen similar feats in medical diagnosis, where truly expert skill and intuition can replace "critical thinking."
Of course, one of the things that makes these people stand out is that they tend to be geniuses of the first water. And they're often capable -- if rusty -- of doing "critical thinking," but they've taken their work to a high enough level that critical thinking is of less importance to what they do personally than it is to the field as a whole.
No reputable doctor would
tell you to diagnose on the basis of intuition. But no competent, experienced doctor would ignore her intuition, either.