I am not so sure. It's not just about solving the problem, but sometimes it's also the willingness and mentality to tackle something that's outside your comfort zone, as well as the approaches.
For example, given the loop in linked lists question, even if a candidate is not able to solve it completely, a reasonable approach would be to break the general case to more specific, trivial cases, such as: what if the loop has known length, what if the loop starts at a known location, etc. Interview questions are not binary decisions, you can learn a lot from a candidate just by seeing how they respond to a question.
(Just to be clear, as this is a permanent and public record, I'm perfectly capable of doing this kind of thing. It's not really an unreasonable question to ask. I'm just being facetious because it's friday afternoon.)
For example, given the loop in linked lists question, even if a candidate is not able to solve it completely, a reasonable approach would be to break the general case to more specific, trivial cases, such as: what if the loop has known length, what if the loop starts at a known location, etc. Interview questions are not binary decisions, you can learn a lot from a candidate just by seeing how they respond to a question.