Permissions error message using Profile (gid=12) in Online Registration

The following Message is returned when Users click on the Link to register for an Event.

"Sorry, due to an error, we are unable to fulfill your request at the moment. You may want to contact your administrator or service provider with more details about what action you were performing when this occurred.

The requested Profile (gid=12) is disabled OR it is not configured to be used for ‘Profile’ listings in its Settings OR there is no Profile with that ID OR you do not have permission to access this profile. Please contact the site administrator if you need assistance."

The Permissions for Anonymous users have been set to allow "register for events" and "view event info".
Using the Registration (test drive) the profile is accessed OK. When I also test by sending myself the link by email it also works OK. However for another user (with Data Manager role) the error message is returned.

The Profile (ID=12) is a standard profile – "Your Registration Info" setup for Events.
So I am not sure the message is describing the problem sufficiently. Any suggustions?