Hi,
if your requirement is to see the background jobs and not to delete it, Kindly check with the assignment of S_BTCH_JOB authorization object to users only. No need to assign the authorization object S_BTCH_ADM.
I checked this issue in the same client(not cross client).When i enable the activity Y in the auth object S_BTCH_ADM the user can able to see the jobs given or released by other user.
Regards,
Ramesh.