Despite the title, software was not at fault here. Rather, the paper found a higher than expected false positive rate due to a choice in statistical modeling. The conclusion was that nonparametric tests can avoid the issue.

So, none of the results are truly invalid in the way of a hypothetical software bug, since we know what modeling assumptions were used in the previous studies. Personally, I don't see a major problem, since most fMRI papers are exploratory, and we should be reproducing the major findings anyway. We should certainly start using nonparametric tests from here on out though!