We may be mishearing their intended formulation, which could have been asking for the longest common substring (described here: difference is that subsequences don't have to be entirely contiguous, just in the same order.)
That's an interesting problem with some simple solutions worth understanding. I don't think it would be unrealistic to expect a high-quality programmer to be previously familiar with it, or, if not previously familiar, to be able to make progress toward the DP solution with some thought.
That's rough, asking for a solution to an NP-hard problem over the phone? http://en.wikipedia.org/wiki/Longest_common_subsequence_prob...
Or maybe they were just expecting you to say "for each combination of subsequences of each string, check if they are equal ..."