When messaging system between site users is disabled, the lines generated when creating notifications in the mdl_notifications database are such that timeread = timecreated, whereas one should have timeread = NULL.
This means that the user is not alerted when new unread notifications are received.

An example to reproduce the bug :

• As a admin, in "Advanced features", disabled messaging system and save changes
• Check for a student that in "Notation préférences", Web notifications for the forum are well activated 
• In a forum where this student is subscribed, the teacher writes a message
• Wait editing time delay and the next cronjob
• Check that, in the mdl_notifications data table, the timeread field of the notification record of the message sent by the teacher and received by the student contains the same value as the timecreated field
• Log in as the student and check that the new notification is not highlighted with a number in the notification menu at the top of the screen.