A few readers emailed us claiming they had been banned from Diablo III while playing on Linux. The complaints about this were being voiced in a lengthy forum thread on the official forums, too. Blizzard replied to us, and on the forums, claiming that people were only being banned for cheating, not for simply playing Diablo III on the open operating system: "Playing the game on Linux (although not officially supported) and/or using Wine will not result in being banned, but cheating will. We’ve extensively tested various scenarios related to this situation, including replicating system setups for those who have posted claiming they were banned unfairly, and have not found any situations where players were banned solely for using Linux or Wine."
They seem to regard that as the final word on the topic.