They could have single player and not allow that character or items onto the auction house.
It's quite easy to set that up from a developer standpoint. They are simply alienating their fans and paying customers because they don't want to lose ANY money. It's the worst kind of DRM and it will hurt their bottom line in the end. As a matter of fact, games that use no DRM tend to make more money because more people buy the product. This might not be the case as Blizzard is popular and Diablo is a huge title. But overall, the average is higher for programs/games with no DRM.
I think that if you want to play single player, an internet connection can be required. BUT... You shouldn't have to have a live connection to play solo. Even if you wanted to forbid that character from using the live servers later, that would be acceptable. Then people could cheat all they wanted in single player, and not affect online at all. Pirates still would be able to pirate, but they will not be able to affect the auction house at all.
I find this to be an unacceptable way to run this game. But I will still play it when they fix their issues.
Side note.. They need to have 2000 more LOGIN servers placed around the world. Load balancing... You would think a company that is this old and with as much money as they do, could handle 50 billion hits a second. Ask Google for some help... They do it daily.