I can construct a test for Kendall's tau correlation coefficient by using a test statistic that is the proportions of "consistent" movements between X and Y (i.e. basically Kendall's tau) and using a permutation test to approximate a sample under the null. No one would argue that the proportion of consistent movements is not, in some sense, linked to the evidence for a "positive" relationship, but that alternative -- in terms of the population -- is not clearly defined.

In general, a clearly-defined alternative only crops up in parametric statistics. In non-parametric statistics things get much less clear, and the alternative has to be specified as a broad family. This is at once its weakness and its strength.