From an engineering standpoint, premium gasoline is specified due to the high compression ratio of the engine. Basically, the fuel/air mixture is "squashed" more as compared to a lower compression ratio engine. At higher compression ratios, the fuel has a tendency to spontaneously ignite, without the benefit of the spark from the spark plug. When this happens at any point other than top dead center (piston is at the absolute highest point of its travel), the engine will not be able to perform at its best.
The engine computer can help mitigate some of this but bottom line is that engine knock is bad. Think of it this way: if one was to go up to an engine and manually turn the crankshaft, you would see all the cylinders move up and down at different times, but all in some sort of synchronous motion. Proper ignition of the fuel/air mixture forces the pistons downward in their cylinders to turn the crankshaft. When this ignition happens prematurely (say from a lower octane fuel), you now have an explosive force trying to push downward on a piston that is supposed to traveling upwards, reducing power and introducing stresses within the engine that should not be there.
Could one get away with mixing gas? I would say in most situations where you're not max-performing the engine (think steady highway cruising) then any damage would be minimized. However, heavy acceleration, stop-and go traffic situations are cases where I would not skimp on the required fuel. It's good insurance if you plan on keeping the car.
Now sticking premium gas in a car that doesn't require it is, in my opinion, a waste of money. There might be some subtle difference in detergent additives among the different grades (company depending), but that's about it. One situation where this would not be the case is an older car that knocks or pings under acceleration. You can mitigate this with a higher octane gasoline.
So, after much rambling, if the owners manual says you need 91 octane or higher fuel, you need 91 octane or higher fuel. Regardless of what you hear some schmo say on the internet. ;)