Purchased through iTunes as well as "Digital Copy" files are linked to your iTunes account, and will only play in iTunes that is "Authorized" to your account. The Droid (as well as all other non-apple devices) does not have this activation system, and will not play these files. Even if you transfer your purchased videos to a different computer with iTunes, if that computer is not "Authorized" with your account, it will also not play those files.
TuneBite, as well as other commercial iTunes DRM removal tools run on your "Authorized" computer, and play the file while recording, similar as dubbing VHS tapes or recording a VHS to DVD using a standalone DVD burner.
In my opinion, it is easier to just rent the DVDs and convert them.