I think the following thread should fully answer your question:
Just note that the bug mentioned there where Picard cannot get the genres other than those directly on the release will be fixed soon with the next server update and an updated version of Picard.
Just wanted to put this right, because this is a common misunderstanding: There is no MusicBrainz 2.1.2. There is MusicBrainz, which is the name of the open metadata database you can find and contribute to on MusicBrainz.org
Then there is MusicBrainz Picard, or often just Picard, which is a music tagger allowing you to tag and organize your files with the data from MusicBrainz. The current version of Picard is 2.1.2, this is what you have installed. And while Picard is the “official” tagger from the MusicBrainz project, it is not the only one. Plenty of other music tagging applications make use of MusicBrainz.