Hi GMFH!
Either you misunderstood me or I didn't get you corretly but barbarians surely can build agricultural buildings in provincial capitals. But, as you said civilized peoples then will only be able to convert them to industial buildings. Or dismantle them and build something else.
In case you still don't believe me:
EDIT:
OK, after re-reading your post carefully I got it!
You meant "non-barbarian factions can not..." and I read it like "no, barbarian factions can not..." ...
Your way of expression kind of confused me but we actually said the exact same... still error on my side