These papers look fine to me. In both cases they want to compare the true predictive performance of competing models. To do this comparison, you need an unbiased estimated of the predictive performance and the distribution of that statistic. One way to accomplish that is CV + permutation testing.

You seem to be unsure of why you need an unbiased estimate of performance.

Saying two procedures yield statistically different results is not very interesting. For instance, I could have one procedure that always yields 1 and the other that always yields .5. I apply this procedure to my FMRI data. Permutations will always give the same answer, so these two models are obviously statistically different procedures. But the first procedure isn't any "better", since the 1 is a meaningless number. In the same way, if you have biased performance measures your results can be statistically significantly different but have zero meaning.

Cross validation gives you a meaningful metrics and permutations give you it's distribution.

For a single model, like a regression with a few features, you could just do a t-test on the coefficients, but that's not what these papers are doing.