Can the Time Capsule serve an Apple TV without a powered on Mac? We have an Apple TV (3rd gen) and a 2 TB Time Capsule on which we know how to store movies already. One can use the Time Capsule and simply add movies stored on it into the iTunes library.

However, how could we use the Apple TV to play media content from the Time Capsule without having to run iTunes on the Mac?

NB: we want to cut out the middle man, so suggesting to use iTunes on another OS doesn't really answer the question :)
Sorry this is not possible without an intermediate device or jailbreaking the AppleTV to run xbmc. Not sure what the policy on this site of advertising jailbreaking links so i'll leave this for you to search.

By default the appletv is looking for a shared itunes library either through the old network advertising method or more recently the HomeSharing method.

The Timecapsule can only present the files via AFP if the disk is formatted as HFS and SMB/CIFS if it's formatted as FAT.

By using xbmc you can mount smb network shares. ie. forum.firecore.com/topic/4116

Of course the other method but still requiring an intermediate ios device would be to download something like VLC and airplay the content. But this doesn't meet your requirements.