Tried it out the other day on an -400F originally delivered from the Boeing factory to CI.
Over Japan, so 7 degrees mag variation. When the sw was flipped from NORM to TRUE, the RMI compass card ( installed CA's side only) rotated the 7 degrees, so card reads true heading ok, but both VOR needles flagged, as you experienced. But when the VOR /ADF needle was selected to ADF, the nav flag withdrew and it did point to the AM radio station correctly.
Maybe the assumption in airplane logic is that VOR's are not referenced to true, though a few are, as you point out?