I am running a 100% stock OpenFire install (to facilitate troubleshooting).
The only configuration change I make after install is to enable debug logging under:
Admin Console:
Server Settings
Message Audit Policy
Enable Message Auditing
Packets to Audit: (all)
The default settings for Group Chat appear to be:
Admin Console:
Group Chat
Group Chat Settings
Room Creation Permissions: Anyone can create a chat room
Default Room Settings (selected):
List Room in Directory
Can anyone discover real JIDs of occupants
Allow Users to register with the room
Log Room Conversations
I think that is default, though I admit I have done testing on the current VM so I may be wrong, but I have definitely tested with the defaults on both the working and non-working versions. I do not currently have "allow occupants to invite others" checked as it's not the default, and it wasn't enabled previously. I have, however, tested with it enabled as well. Even if it is off, though, the person requesting the room is owner by default, and should be able to invite anyone.