Sure, it could have perfectly properly been a brief amici curiae, just as briefs of neuter entities (e.g., colleges) are amicus curiae briefs rather than amicum curiae briefs, and “brief of amici curiae” doesn’t get turned into the genitive “amicorum curiae” — law Latin isn’t Latin Latin (thank Jupiter). Still, a pleasant bit of linguistic fussiness; I found only a handful of other amicae curiae briefs in my Westlaw search.
Thanks to my brother Sasha for Latin consulting; all remaining errors are the fault of residents of Soli.