Usually, but not necessarily... It comes down to cylinder pressure. Later closing intake and exhaust timing built into your cam will reduce the resulting cylinder pressure and allow you to run a higher compression ratio - without fear of piston/valve damage.
Higher compression ratio's combined with valve timing that creates high cylinder pressure absolutely requires higher octane fuel...
As always, it's the combination of all the pieces.... 
What Scott's talking about is static compression vs corrected compression. The physical piston, squish, and head volume may calculate to 10:1, but when you add in over lap and exhaust timing of the cams the compresion may be in the mid 9's. What you want to know more than CR, is like Scott said, the cylinder pressure when all is said and done. Here's a chart, I think from Night Rider.
Static Cranking Pressure Performance Implications
Less than 115 PSI Poor low speed performance, poor throttle response, hard starting. Compression Ratio and Cam not matched or worn rings, valves.
120 PSI to 145 PSI Expected range for most stock or modified street motors. This is a good range for a street motor.
145 PSI to 165 PSI Modified street motors. Static pressures in this range should produce good results. This is a good range for a street motor.
165 PSI to 180 PSI Marginal for street motors. Possible hard starting, detonation and overheating.
Over 180 PSI These are all out race engines. A street motor in this range will be trouble. Stick to the track.
Craig