Energize - I do agree with you.
If he is literally "backing up" then he is creating a duplicate on the external disk. This should then allow for coffee being poured into the external disk and still having the original on the PC.
But there are people who say "backup" when they mean "archive". This is when they want more space on the main PC and they delete files after they are backed up. That is what I was warning against.
For important photographs of the kids, etc, it is still worth backing up to DVD and then send the disks to a relative to look after. If your house gets burgled, or the PC burns up in a fire, then any backup disks stored near by will also be gone.
Expect the unexpected. I usually quote the example of the Twin Towers in New York. Most of the companies based there would backup to the other tower as they
knew the data would be safe as nothing could happen to both towers at the same time.....
When I do my backups and archives, I spread duplicates around my servers and various hard disks. Then make specific backups to DVD of the most valuable data. I don't bother making DVDs of my music. But I do make sure I cook all photos and business documents.
(BTW - I had to laugh at your comment of "low capacity" of a DVD. I remember having to backup to 1.4MB floppy disks.... Ouch!!)