Yeah that is a big red flag - as the OP mentions, there is basically no way of making k=2 statistically different from k=1, that's why nobody uses it.
I suppose the authors just tried many different k and selected k=2 because it performed surprisingly well (likely due to the bug the OP found out). But if the results were significantly better than k=1 or k=3, it's a bit weird the authors never double checked why that was the case. I guess it can be one of those things you settle on early in the overall process with a few experiments, and just take for granted afterwards, never checking it again, but still, it sounds like something that should pop out at some point while writing the paper...?
I suppose the authors just tried many different k and selected k=2 because it performed surprisingly well (likely due to the bug the OP found out). But if the results were significantly better than k=1 or k=3, it's a bit weird the authors never double checked why that was the case. I guess it can be one of those things you settle on early in the overall process with a few experiments, and just take for granted afterwards, never checking it again, but still, it sounds like something that should pop out at some point while writing the paper...?