Suddenly it worked.
DAVDroid 188.8.131.52-ose fails to sync some contacts that are on ownCloud
I compare Sync results with Evolution, presumed to be accurate:
This is clearly broken
It is also the case that DAVDroid does not sync everything at once. You have to sync repeatedly until the sync finished almost instantly.
Evolution displays contact counts if you select an account in the left pane
Google Contacts (6.0.1+) displays counts if you go Contacts - ⋮ - [CardDAV account name]
Older contacts displayed a total count at the bottom of the contacts list
In between versions display no count at all