Re: Loving it for all it's flaws
The connection required thing was definitely true of 3, and I'm pretty sure of 2. It's the reason I won't buy 4 until they remove it.
For no apparent reason on 3 (and Arkham City and Arkham Origins), I've occasionally been informed that I've lost connection to their servers and lose all progress beyond the last checkpoint, which can sometimes be a long time ago or just before a difficult fight, etc.
For Arkham City (with the dreaded Windows Live integration), it actually completely corrupted my save, so I stopped playing.
Buying the game and getting a cracked copy is definitely easier than living with their failed attempts at DRM.