That’s a security thing controlled by the browsers. Gives people a chance to view a link before clicking as to avoid suspicious links that may have things like malware.
So I don’t believe, at least I’m not aware of any way to hide it.
If anyone is interested, I found out that I had a stack that makes it possible to offer files for download without making the link appear in the status bar.
The stack is True Download, by Doobox, and I just bought True Download 2 which is a little better.