The static compression doesn't mean as much today as it used to. My Pontiac GTP (supercharged) was only 9:1 but the supercharger supplied a constant boost pushing it up much farther so the numbers didn't mean much.
On turbocharged engines, it's is essentially the same. The turbocharger forces more air into the cylinders, so a 10:1 engine becomes 11:1 or 12:1 effectively. That in turn requires higher octane fuel to prevent pre-ignition. Higher compression = more heat. (PV=nrT) So the static compression is increased by the turbo boost, and the computer monitors all that and controls the boost along with spark timing to prevent pre-ignition as detected by a knock sensor. It's all quick as a millisecond and very effective, but reducing boost reduces power, hence the need for higher octane. A tank or two of low octane in an emergency won't hurt, but you won't get the power of higher octane. In many parts of the U.S. at higher altitudes, the "premium" octane rating is several points lower than at lower altitudes. This is unfortunate for drivers with superchargers or turbos because we don't need the lower octane fuel at thin air at higher altitudes which cause over-lean conditions on normally aspirated engines. All turbocharged engines that I know of from virtually every manufacturer require higher octane fuel.