Often the text in a paper that describes some algorithm will not be completely clear or complete. Providing the code fills in those blanks. I've taken a paper with code and gone through the code line by line comparing it with what was described in the paper. The code often ends up clarifying ambiguities. In some cases there's an outright disagreement between the paper and the code - that's where the feedback comes in, ask the author about these disagreements, it will help them clarify their approach (both the text and the code).

> Reproducing the results does not mean running the same code as the author and plotting the same figures as in the paper.

Sure, to some extent. But the code does provide a baseline, a sanity check. People who are trying to reproduce results should (as I describe above) go through both the paper and the code with a fine tooth comb. The provided code should be considered a place to start. I'll often re-implement the algorithm in a different language using the paper and the provided code as a guide.