That depends: if they will need to write C code, then of course, they need to know the language. But if all they're gonna do is write Haskell, Erlang or Lisp, what's the point of knowing C?
I do know a lot of people, who are excellent programmers, but their C is read-only at best, because their language of choice has been something else.
I see nothing wrong with that. A good programmer usually doesn't think in a language context anyway, he translates his thoughts to a language, yes, but when designing, he thinks a few levels above the language. Thus, the lack of C knowledge does not, in my opinion, does not mean one's insufficiently skilled. Nor does good knowledge of C mean one's a good programmer.
I've also met with people who were excellent C coders: they could code down whatever they were told to, blazingly fast, using every trick the language had to offer. But they couldn't design their way out of a paper bag, because they lacked vision: they could only think in C, and not beyond that. They couldn't see the bigger picture.