The whole shenanigan was started on Blizzard's official forums by some gamers complaining about being banned after playing Diablo III on Linux.
Blizzard has replicated the setups described by the users and tested their own system, and Linux clients were not banned. The company has said plainly that they are not banning the Linux players, only cheaters.
“We’ve extensively tested for false positive situations, including replicating system setups for those who have posted claiming they were banned unfairly.”
“We’ve not found any situations that could produce a false positive, have found that the circumstances for which they were banned were clear and accurate, and we are extremely confident in our findings.“
“Playing the game on Linux, although not officially supported, will not get you banned – cheating will,” a Blizzard statement said through their forums.