Allowing Team members to reassign tasks to themselves

Hi.

We have a team member that is going through a medical treatment that may require him to be out of the office unexpectedly.  So to insure that the department has visibility into any tasks that are assigned to him and allow his coworker (coming in from a different department, just popping back into this department to help when needed) I would like to assign project tasks to be a team instead of the individual worker.  For my example, we have Guy A  and Guy B, who make up Team AB.  I want to assign queue requests (issues) and project tasks to Team AB, then allow Guy A and Guy B to go in and claim the task/issue with the start work button.  This works for the queue requests (issues) but not for the project tasks.  They recieve a notice that they do not have sufficient access to reassign the task.  Short of making them a system admin, I have given them every level of access I can find.... what am I missing?  Do they have to be a system Admin to reassign project tasks to themselves? Do I need to redo a setting on everyone of our projects individually?