Hi
I'm not sure that this is normal behaviour. (Otherwise, what would be the point in this method?)
I use the same backup method as you as I don't have SSH and can't CHOWN (same as you).
I however, don't have a problem downloading from my backup folder.
Although, on one occasion, I was just about to upgrade my forum when I found I couldn't backup my gallery
(see this thread).
This had never happened previously, I wonder if you are experiencing the same 'glitch' (or perhaps 'bug') as me?
I got my hosts to reset the permissions and it's been fine ever since.
So just a thought, ask your host to reset the permissions and then try another backup.