Tried to duplicate the problem, but it worked fine...
Code:
vindsl@Zuul:~/Downloads/Ubuntu$ zsync http://cdimage.ubuntu.com/daily-live/current/raring-desktop-i386.iso.zsync
#################### 100.0% 239.5 kBps DONE
No relevent local data found - I will be downloading the whole file. If that's not what you want, CTRL-C out. You should specify the local file is the old version of the file to download with -i (you might have to decompress it with gzip -d first). Or perhaps you just have no data that helps download the file
downloading from http://cdimage.ubuntu.com/daily-live/current/raring-desktop-i386.iso:
#################### 100.0% 397.9 kBps DONE
verifying download...checksum matches OK
used 0 local, fetched 807711061
vindsl@Zuul:~/Downloads/Ubuntu$