I believe Avenue is referring here to the sui generis database right (in http://en.wikipedia.org/wiki/Directive_on_the_legal_protection_of_databases the section sui generis, not the one "Copyright"). This only exists in Europe.
Database rights are relevant for new data imported into Wikidata by Europeans from those European databases that have no license which addresses database rights (such as CC0, ODbL, etc.).
As far as my analysis goes, they do not affect Wikipedia, however. The database right protects the database as a whole, not individual records (although records can be protected as part of the database). The database right for the database as a whole is automatically given to the employer or the single person creating the entire database. Both cases do not apply in the case of Wikipedia. WMF is not European, does not employ editors, and most likely none of those editors which reside in the EU can claim to have created an entire and complete database.
I am not a lawyer - please correct should my analysis be wrong.
Gregor
(PS: The fact that the unported CC 3.0 licenses are silent on database rights, whereas several ported (de, fr, nl) explicitly waive database rights is a known issue and under discussion in the CC version 4.0 process.)