If you follow their methods, specifically [63], they are modelling the proportion of null hypotheses in their tests. Performing FDR by group is a reasonable approach, and does not necessarily cause P-value inflation. This is different from a Bonferroni correction, in which total numbers of tests done is the only factor. These FDR models of the proportion of null hypotheses rely on the distribution of p-values, not their raw count (assuming a sufficient count of P-values is present in which to model). Dividing the FDR correction as they did provides more information about group-specific influences, and should not be considered p-value hacking.

Nevertheless, thank you for calling this out. There is way too much p-hacking in science, especially biology.

[63] Benjamini Y, Krieger AM, Yekutieli D (2006) Adaptive linear step-up procedures that control the false discovery rate. Biometrika 93:491–507.