Recognizing the pattern is the problem solving part of the problem.

I think the argument is that recognizing the algorithm part through the (usually thin) facade is very easy, once you know the (common) DS&A questions well. I.e. there is a lot of challenge in learning the algorithms, and little to no challenge in recognizing it through the problem. Examples where a person knows the underlying DS&A very well but is unable to recognize the nature of the problem would be a great counter argument.

Yes but there is an infinite number of ways to ask the questions.