Of course, you need people on site who can properly define the word 'problem'. I've gotten some very late night calls for severely stupid, non-critical issues.
Totally true story.
One of my co-workers at a prior job called Tech Support at 11:30 on Sunday night because "all capitals are coming out."
Explanations were not accepted, nor was advice over the phone. IT actually had to send a tech to press her Caps Lock key.
They used to call us to tell us that the backup failed because the tape drive isn't working.
It is hard to say what they expected us to do.