I found the solution:
Brainstorm calls to import ?h.BA.label by default, which is deprecated after 5.1. FS5.1 and after creates BA labels under ?h.BA_exvivo.label.
In our dataset, we ran it through 5.1 then to 6.0. The vertices between the ?h.white/pial are different between 5.1 and 6.0. Brainstorm is retrieving the 6.0 ?h.white (which FS overwrote the 5.1) and the 5.1 label, hence the error.
A suggestion for Brainstorm developers is to retrieve the exvivo labels if both the exvivo and the deprecated label exist.