I finally got BackupPC working under Centos-7.1 after several hours of pain. I had been running it for several years under CentOS-6, and probably CentOS-5, but there seem to me to have been several new issues that arise with CentOS-7.
In my experience, the official documentation on this, http://backuppc.sourceforge.net/faq/BackupPC.html, is more or less useless unless you have a very long time to spend. It suffers from the usual Linux disease of having inordinately long explanations of everything with no examples of the actual commands a real person has to give.
The explanation in https://wiki.centos.org/HowTos/BackupPC (which I only found later) is much better, though it starts with the warning "This page is no longer maintained, having been abandoned on 2009-09-17".
I thought I'd write a 1-page note to myself of the steps I took, in preparation for CentOS-8... I have a couple of questions that this raises.
1. Why exactly does backuppc want to ssh to root? Is this just a way of running BackupPC as root?
2. The graphical interface seems to be treated as an extra, but what other way is there of accessing BackupPC? Is there a CLI approach? If so, where is the list of transfer requests kept?