Thanks again. Message is clear though, whether chicken or egg, … FIX any corruptions, for sake of integrity of backups if nothing else.
Yes, and you definitely want to get DiskWarrior. Disk First Aid refused to repair the disk, but no problem for DiskWarrior. Be aware that DW will take a long time (like several hours for a 3TB disk) to rebuild a Time Machine directory due to the huge number of links.
For those who don’t know, Disk Warrior is not a universal disk repair tool. It only does one thing (rebuild the directory structure of HFS+ volumes), but it does that one thing better than anybody else and is therefore a critical tool to keep in your toolbox.
You will still want other tools (including Apple’s Disk Utility/fsck) for repairing other kinds of damage. Especially on APFS volumes, which can currently only be repaired by Apple’s tools.
And, of course, no amount of repair tools are a substitute for a good backup strategy because sometimes the damage is so bad that the only practical option is to erase the volume and restore the files from a backup.