Forum Members can't view a single moderator's visitor messages
 

I can't seem to find an option where to disable/enable viewing of visitor messages by user.

One single member's, who is in the moderator usergroup, visitor messages cannot be viewed by any other members who are not Moderators/Super Moderators/Administrators.
This user has "Limit usage of Visitor Messages to Contacts and Moderators" set to No
"Visitor Messaging" set to yes
Moderators/Super Moderators/Administrators can view visitor messages of this user OK, just not regular members.

Other moderator's visitor messages can be viewed by anyone, so it doesn't appear to be a usergroup error.