I have limited (read none) experience with Oracle.
I've never heard of the term "Oracle database synchronization", so I've not idea what your DBA might be implying with regards to that.
As for a crosscheck, then yes, I would have thought that a DBA would want to (but does not need to) perform a cross-check after a failed backup. A "cross-check" is essentially about the Oracle database itself asking/querying/probing the MML (Media Manager Layer) (i.e. NetBackup) for a list of known (i.e. still retained) backups, so that Oracle can adjust its own view of what is still retained, so that Oracle can determine (if required) which elements of pre-existing data needs to be backed-up again, or new data that needs to be backed-up for the first time ever. Essentially, the requirement as to whether to perform a cross-check is always down to how the DBA originally configured their backup jobs in the first place, and down to how those jobs continue to run day-to-day. IMO, only an Oracle DBA can know whether they need to perform a cross check or not. Normally a "backup" admin/engineer is not concerned about how or why or whether an Oracle cross-check needs to be performed or not... unless the DBA starts to run too many cross-check jobs. (BTW: a cross-check job in Oracle speak is synonomous with a bplist in NetBackup speak) (and a bplist in turn causes a query via bpdbm).
