Are they the owners of their groups (identified by star next to their name in group members list in Persona)? Because even if they're not moderators I believe group owners are able to add people to their group.
@julian I found this after re-reading the NodeBB NGINX configuration docs
nginx must be on version 1.4.x to properly support websockets. Debian/Ubuntu uses 1.2, although it will work there will be a reduction in functionality.
Previously, in the same doc:
NGINX version v1.3.13 or greater
I'm not sure if that is just a sign of an outdated doc, or if there is actually some type of incompatibility (which apparently doesn't surface everywhere). All I know is that by reverting to 1.4.x, all functionality was restored.