This month a story was making the round of gaming blogs that Blizzard was banning players for cheating in the single-player part of Starcraft II. That turned out to be not totally true: Starcraft II has a built-in cheat mode, and using that is perfectly legit. What Blizzard does is banning people for using third-party cheat software, which could potentially be used both in single-player and multi-player mode. Furthermore third-party cheat software in single-player mode could be used to get achievements which are visible in multi-player. The people who launched the "Blizzard is banning players for cheating in single-player mode" story just happen to be the people selling the third-party cheating software, so the first versions of that story weren't quite as balanced as they could have been.
Cheating in multi-player is a problem, and nobody is more aware of that than Activision Blizzard. While Blizzard is doing quite a good job of keeping World of Warcraft free from cheaters, the Activision part of the company bungled that issue for Modern Warfare 2. MW2 is reported as having become nearly unplayable in multi-player due to widespread cheating.
On the other side is a huge number of players who think that cheating in single-player mode is perfectly okay, having spawned a huge industry of cheat codes and third-party cheat software. A Google search for "cheat" turns up 63 million hits, most of them about video games. Games like Civilization V even come with big toolboxes enabling players to "mod" the game in any way they want, which includes ways to make the game much easier. There is nothing that stops you from making a Civ5 scenario in which you start with a tank against the AI opponents' spear men.
So the question is whether a company has the right to ban players from using cheat software, even if that software isn't actually used in multiplayer mode. The Blizzard Warden anti-cheat software takes a "better safe than sorry" approach and reacts to players having cheat software installed, whether it is used or not. Probably the Starcraft II anti-cheat software is based on similar principles.
Ultimately we have to ask ourselves whether a game which requires you to be online to play it and which has lots of online functionality like achievements and such can truly still be "single-player". What use is an achievement system visible to other players if it is allowed to be manipulated?