Agreed, but it is apparent that the backup(s) that are failing are failing because the database(s) are active as mirror databases not the principal database(s).

When I configured my databases to use mirroring I had processes in place to enable or disable the backup jobs as appropriate depending on the state of the databases on the servers.

The only backups that were active on both servers were the backup jobs that backed up my system databases. There were no other active user databases on my mirror servers. These were dedicated to provide HA for production databases.