Those methods still rely on correlation. To be clear: We are not only talking about linear correlation here, which is only one of several kinds of correlations.
Another example: mendelian inheritance patterns in a pedigree study.
If you know of a good measure of non linear correlation please let me know. And publish a paper in science or nature like the MIC/MINE people did (a measure that has issues in practice).
In using those methods you may never calculate correlation as a number, but when those methods find something you still rely on the fact that there is a correlation.