"When I removed the plates I found that the electrical boxes were not
attached to the studs, instead *they* were attached directly to the
back of mounting plates using a threaded tube and strap".

I still don't understand the installation, even after seeing the photo.

My question was (and still is) is whether or not the original
installation method was acceptable.

If you remove that front diagonal strap, is the box loose in the wall? If
so, that is not a normal installation. As long as the box is secure when
everything is tightened down, it shouldn't matter. But thinking ahead to
future fixture replacements that may have different mounting systems, I
would find a way to secure the box without the front strap.

Anthony Watson
www.mountainsoftware.com
www.watsondiy.com