As designed, you must have the Manage all tasks operation to be able to reassign tasks. However, someone without this operation was able to reassign an already assigned task from the My tasks and reviews > Unassigned window. The issue arose when people were simultaneously looking at the same unassigned tasks list and self-assigning the same tasks within the same period of time. One person's list would not refresh immediately, potentially resulting in a stale task list. As a result, people were able to reassign a task to themselves using Assign to me, even though someone else had already self-assigned the task.