Hello,
The owner of a task is the current assignee. The bpm:assignee property is actually for a task input by which the current assignee can set the assignee for the next task, i.e. when he has been assigned a task where he must decide who will be the next in line to process the workflow. As long as you don't include the bpm:assignee property or its aspect in your task model, you will never see it in your task properties at runtime.
Regards
Axel