I’m guessing based on a quick view-source check you are using buddypress. Have you looked into other plugins to the site. Buddy press appears to have a plugin related to private messages. Search up the following in Google it should help. Plugin gives options for admin or user to be able to control who can send PM’s. Not sure if that’s definitely same thing but if it is could be a good work around to the issue.
<h3>Plugin – BuddyPress Restrict Messages</h3>
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