I tried to go through all the relevant evidence provided in the Blizzard forum post by the affected player (Jarrex), and here's my interpretation:
As far as I can tell, Jarrex gave links to three different websites where people posted their linux/banning problems:
Site 1. an /r/diablo3 thread :
Posted by user "km1tche11", no replies reporting similar experiences
Other replies state that they are using the same setup, but have not been banned.
Site 2. a winehq thread
:
Posted by user "william", looks like 2 or 3 other users reply with similar experiences, one with the username "Mitch"
and Site 3. a playonlinux thread
In the /r/diablo three thre
Posted by user "Mitch", one reply with a similar experience from user "fabioshot".
Other replies state that they are using the same setup, but have not been banned.
All the concrete evidence point to only a small handful of users experiencing permabans, and a high probability that at least one of them posted in multiple forums ("Mitch" - playonlinux, "Mitch" - winehq, and "km1tche11" - /r/diablo3). Additionally, the original poster in the Blizzard thread demonstrates some knowledge/interest in the banning practices of Valve and Blizzard (not necessarily damning, but interesting). Otherwise, all the other posts (at least in the Blizzard thread) are either worried Linux/WINE users, conspiracy theorists trying to convince everyone else that Blizzard is teh evils (usually the ones with high-level WoW avatars...go figure), or just trolls in general.
TL;DR - Most likely multiple assholes trying to get away with cheating in D3 by raising a stink among Linux/WINE users. Move along, nothing to see here. Please don't feed the lying, cheating trolls.