The only way the users have to reload a document on the server is making them Document Administrators in the QMC, so they can get to their corresponding part of the QMC and create a new task.
Apart from that, clients do not allow reloading, either it is Desktop, Open In Server, Plugin or Ajax.
Then there is EDX, that means that using a third party software and calling the QMS API any user that is able to see the object with the action that triggers the task is able to actually run the task. Say that you have a button object with a show condition that is only true for a given list of users, for example:
Match(OSUser(), 'DOM\USER1', 'DOM\USER2')
As only users 1 and 2 can see the object, they are the only ones allowed to call the EDX task.
Hope that helps.