>"All of the analyses to this point have been based on resting-state fMRI data, where the null hypothesis should be true."
They are not careful to explicitly define this null hypothesis anywhere, but earlier in the paper they describe some issues with the model used:
>"Resting-state data should not contain systematic changes in brain activity, but our previous work (14) showed that the assumed activity paradigm can have a large impact on the degree of false positives. Several different activity paradigms were therefore used, two block based (B1 and B2) and two event related (E1 and E2); see Table 1 for details."
This means that they actually know the null model to be false and have even written papers about some of the major contributors to this:
>"The main reason for the high familywise error rates seems to be that the global AR(1) auto correlation correction in SPM fails to model the spectra of the residuals" http://www.sciencedirect.com/science/article/pii/S1053811912...
If the null hypothesis is false, it is no wonder they detect this. In fact, if the sample size was larger (they used only n=20/40 here) they would get near 100% false positive rates. The test seems to be telling them the truth, it is a trivial truth, but according to their description it is correct nonetheless.
Edit: I was quoting from the actual paper.
http://www.pnas.org/content/early/2016/06/27/1602413113.full