The bead isn't gonna be any bigger with the tyre the wrong way around, so why anyone thinks it's more likely to pop off the rim is beyond me. Likewise with the rest of the structure, which is the shape of a horse shoe, and will still be the shape of a horse shoe when inverted.

Couple of exceptions spring to mind;

Any radial ply will be on the inside.

The inner layers will be tighter, so these will be susceptible to split stress on the outside - likewise the outer layers on the inside will be compressed and bunched, risking deformation and splitting from the afore-mentioned layers.

The heavy tread is likely to damage the tube - use a thin slick tyre for this.

The inner wall, now on the outside, has a layer so thin it's literally just painted on. Therefore it'll make no useful form with the road surface.

All in all you're looking at a tyre with no grip, reduced structural stability, Risk of total failure at the weave.. but I see no reason why the bead would leave the rim unless it was already well off-centre when the tube was inflated.

I also see no practical reason for doing it. Surely if a tyre is damaged that much on the outside, turning it around isn't going to improve anything...