Think of it in terms of interfaces.
The problem is that the heat transfer into the paint layer is primarily by conduction. The paint layer then acts (more or less) like a black body radiator. If you’ve ver seen an infra-red picture of -well, anything- you know that the surface color or treatment generally doesn’t affect its IR radiation too much.
Okay, so you noticed the “generally”, and are asking yourself why this bead paint couldn’t be one of those few special surfaces. Well, without going into a lot of technical stuff, just remember that a photon of IR (radiated heat) starts at roughly 100 nm = 0.1 micrometers wavelength). To a photon, those glass beads are so huge that they are *not" part of the paint layer, but separate objects, like Jimmy Hoffa in a concrete foundation somewhere, or the interface between roof and air.
To the extent that reflected radiated IR (heat) matters at all, it will mostly reflect between the beads and the paint holding them. That won’t help you much. On the small scale of a photon, it’d be like embedding “reflective” silver balls in concrete. That wouldn’t make the cement appreciably more reflective, would it?
If you really want a reflective surface, you might consider one that is far more reflective – like aluminum foil. The atoms on the surface of the foil form an arrangement that is extremely good at reflecting both visible light and IR, as you probably know from cooking and grilling. Stapling aluminum foil between your rafters may look silly, but it’d be cheaper, work better, and you can do it yourself in a hour or two (heed the concerns others have offered, though: roofs aren’t just hats to keep the rain out; moisture/heat trapping are genuine concerns)
Aluminum foil, which is far more reflective to IR than any beaded paint, also offers an excellent test of the limits a thin reflective surface layer (like a layer of paint) to block conducted heat: a single sheet of foil in the air between your hand and hot coals will serve as excellent protection from radiated IR, but pick up a hot coal, using a single sheet of foil as “reflective insulation”, and you’ll burn your hand badly. (If you must do this experiment, use something safer than a coal, like a hot baked potato – or better yet, a cup of hot coffee)
I realize that I’m oversimplifying the science greatly, but I hope these examples will give you concrete confidence in the answers you’ve been getting, in a way that complex differential equations might not.