Why does Yosemite want to throw away all my backups?
When I posted, I suspected that this was specifically related to the Yosemite update, as I'd seen a few hits in Google with similar things (but no fixes), especially since I had already restored the meta-backup meant to address exactly the issue discussed in the older Q's of generic network disk corruption.  

After reading the Troubleshooting post referenced by the older Q, I learn that this message is produced by a verification (fsck) that's run once a month.  This means that whatever anomaly it found was not something that occurred in the previous backup, but could have occurred any time in the last month!  Now, I think the correlation with this “happening” right after the Yosemite upgrade may be that the last-check-date gets lost or it intentionally performs a check right away after installing.  So, any problem that occurred in the last few weeks suddenly is brought to your attention.

If this is checked on purpose, I think it would be better to check before installing the update, to give people a chance to get a working backup of their system before the update.

I rolled back the NAS volume another week, and all was well.  Just let it finish “finding” and then checking the disk.