Right off the bat I'll say it's not the valves, which aren't really directly affected by octane ratios.
The preignition generally happens when carbon built up on the piston (or cylinder head) creates a "hot spot." The hot spot is caused by the carbon holding a higher temperature than the metal, and it gets so hot that it inititates combustion before the spark. This is how a diesel engine works without spark plus by the way. Unfortunately, it's a lot more damaging in a gas powered vehicle because there is still a spark. The spark happens a fraction of a moment after the hot spot starts combustion from it's point. The two burning fronts eventually collide with one another which causes a powerful blast noted as an audible "ping" or "knock" from outside of the engine.
If you have been running higher octane fuel in your car for an extended length of time and you switch back to 87 octane, not only is there likely to be some carbon buildup due to incomplete burning (see one of my posts above), but the computer is also used to the 91 and it's adjusted for it.
Advancing timing causes an issue with lower octane fuel because of the burning properties. Lower octane fuel burns faster and is more explosive than high octane fuel. If you bump your timing too much, you wind up having the piston colliding with the flame front created by the spark. The piston is on the compression stroke, the spark goes off say 15* before the piston reaches the top "TDC" and the flame wave travels so fast, it runs into the piston. If your fuel burns slightly slower, like high octane fuel, your piston can reach the top before the flame front is at maximum force, thereby avoiding a powerful collision inside the engine.
87oct fuel doesn't normall have ethanol, which is generally formulated at 10% by volume in 89+oct fuels. Ethanol has a higher octane rating than gasoline, I think about 104, so adding it is cost effective to increase octane ratings. Ethanol may also burn 50% cleaner than gasoline, but it requires 2x as much ethanol to get the same power as gasoline, so your car burns 2x as much of it. 10% (minimum) formulated ethanol gas will therefore reduce your fuel economy by .10 x .50 = .05 or 5%. That's about 1-2mpg.
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