I understand what you're saying but feel we're comparing different things. Yes, in an interview saying the thing you quoted would obviously be a red flag, and something I would never say. I understand the need in interviews to impress using your problem solving skills.
However, I believe that in your day to day job as a programmer, that quote is more appropriate - that you understand how particular data structures should be used rather than it's inner workings.
In this case, if we assume that the reason you're being interviewed is so you can do well at the day to day stuff, then my quote makes more sense.
I get you though; you want someone who can solve many new problems but it highly unreasonable to put a programmer in an unrealistic situation like an interview and expect them to perform just as well as they would on the job.
Unfortunately I have no answer on how to improve the interview process but it still bothers me that a better way hasn't been found.
Not many people even use linked lists anymore anyways, unless they are programming low-level things and even then it is often more efficient to use a growable array, something like List<T> in .net or vector in C++.
Reversing a linked list is not about how linked lists work. It is a very simple question which verifies that a person knows what the pointers are and how to use them, can write simple loops which manipulate pointers and can handle simple things such as 1 element lists, 0 element lists etc.
I get you though; you want someone who can solve many new problems but it highly unreasonable to put a programmer in an unrealistic situation like an interview and expect them to perform just as well as they would on the job. Unfortunately I have no answer on how to improve the interview process but it still bothers me that a better way hasn't been found.