The as-designed behaviour right now is - when a Company-specific notification is offline, ITSM Notification Engine default to use the -Global- notification and do not actually "disable" notifications as the Company desires. The implementation methodology is that offlining Company specific (or not having a company specific) notificiation is the key to going to the global one.
The desired behaviour is to set a priority on the Customer specific notifications - if they are set, independently on whether they are enabled or offlined, the system should no more search for a Global equivalent. There are several Customers asking for this functionality so it makes sense to include this requirement in future release.
Please look at the ISS04346361, 2-High SupID:479097 - Notification engine not working correctly - for reference