Originally Posted by FBinNY

As I said, simply mounting and tightening the water bottle screw will clinch the nut.

If it's free-spinning, but otherwise OK, you don't need a shop or special tool. Go the the hardware store and buy a long 4x.8 metric cap screw (must be a high strenght cap screw or CrMo hex head screw) a nut and a few washers.

Thread the nut and washers onto the cap screw, Then thread it into the loose riv-nut. Now hold the screw and tighten the nut down against the frame. This will draw the back of the screw up while the washers hold the head down and compress the fitting. It doesn't take a great amount of force, so don't get carried away and snap the screw, and have to come back here and post "how to remove a broken..."