While mounted cifs, backintime is able to create directories but fails to create files.

Time Capsule does not support NFS.  So the default CIFS mount options must be changed.

Thanks to the kind people here for asking the question (although they did not have the appropriate solution):

https://answers.launchpad.net/backintime/+question/93336

And thanks to this thread for providing the answer:

http://backintime.le-web.org/2009/05/10/files-not-copied-when-backup-directory-is-on-smbfs/

The solution is to mount your time capsule in this method (if you have a disk password in place.  otherwise, remove the user,password options):