DubConqueror: I checked the games on the Steam Wikia list against the game I have in my Steam library and found one game that's on the DRM-free list there, that doesn't function completely well without internet:
The Incredible Adventures of Van Helsing does run without the Steam client, but it seeks an internet connection so I tested it with my PC (Windows 7) disconnected from internet and when I do so, the game does run, but when closing down the game after playing, it crashes with the error message 'this program met an unexpected error, it needed to be shut down' displayed, which doesn't happen when the game can connect over the internet. Not completely DRM-free? Though that depends on how you define it, I guess. It led me to finishing the game with the GOG version.
Does the game still work before getting that error message, though? As in, can you still play it, advance, save your data, load your data, etc.? Because if so I'd personally still consider it to be DRM-free, since it does work. If the error message doesn't really do anything, then it can be disregarded.