Incorrect as usual. The reason that Magnagora cannot influence Rockholm and Southgard is because 90% of the village is undead and -only- Magnagora can influence undead. If Glomdoring can influence undead, it will be in the same situation and given that Glomdoring will be tainted and the two former overseer of the forest were undead, we can assume that ability will be available.

From this point forward, when Rockholm or Southgard go into play, the
dwarves there will refuse to be influenced at all by whichever city
controls Angkrag.

Before people start flaming me on the forums for this decision, I'd like
to explain that we've been studying the fact that it is basically
impossible for New Celest or Serenwilde to influence Angkrag because the
denizens there are almost all undead (except for a handful of orc
servants). As this is imbalanced and since the three mining villages of
Angkrag, Rockholm and Southgard are important for metal commodities, we
have decided this is the best solution overall. This should not be
viewed in any stretch of the imagination as 'punishing Magnagora for
doing well' (as I know this is a conclusion some Magnagorans enjoy
leaping to), but rather it was made by looking at the overall scheme of
village influencing.