Branch prediction is related to the Spectre attack. I believe AMD is only unaffected by Meltdown.
I really hope that this is just poor wording and that branch prediction is either disabled in extremely rare circumstances or they just exposed some control mechanism like Intel did which allows you to control the branching.
EDIT:
AMD's response was that mitigation from their side isn't needed for SPECTRE either:
http://www.guru3d.com/news-story/amd-rsponds-on-amd-processo...
I really wonder what has changed, and if now they are vulnerable to variant 2, have they underestimated MELTDOWN as well?
I'm also looking forward for people to look into the victim cache that AMD has implemented with Zen and if InfinityFabric and the added latency between CCXs can't be exploited for side channels attacks.