I think you all missed this in my OP:
"The bike I have is a disk brake model and required the "L" shaped mounting bracket. "
It is impossible to mount that bracket inside, or even the fender mounts as I thought might work. There is no room.
The bolts are not loose and they are made of the standard stainless/chrome/whatever that comes in the mounting kit with. I am not having a similar problem on the wife's bike, same rack (Topeak Explorer), same bolts, just no fenders.