The web can be used as a special remote too.

# git annex addurl http://example.com/video.mpeg
addurl example.com_video.mpeg (downloading http://example.com/video.mpeg)
########################################################## 100.0%
ok

Now the file is downloaded, and has been added to the annex like any other file. So it can be renamed, copied to other repositories, and so on.

Note that git-annex assumes that, if the web site does not 404, the file is still present on the web, and this counts as one copy of the file. So it will let you remove your last copy, trusting it can be downloaded again:

# git annex drop example.com_video.mpeg
drop example.com_video.mpeg (checking http://example.com/video.mpeg) ok

If you don't trust the web to this degree, just let git-annex know:

# git annex untrust web
untrust web ok

With the result that it will hang onto files:

# git annex drop example.com_video.mpeg
drop example.com_video.mpeg (unsafe) 
  Could only verify the existence of 0 out of 1 necessary copies
  Also these untrusted repositories may contain the file:
    00000000-0000-0000-0000-000000000001  -- web
  (Use --force to override this check, or adjust annex.numcopies.)
failed