why turbo cars use low compression?

I could never figure this one out, most turbo gasoline cars use lower compression setups, but wouldn't it be just as effective for a engine to run 15psi of boost with 9.5/1 compression compared to 20psi with 8.5/1 compression, If fact wouldn't the higher compression has the advantage, due to the fact of turbo lag and being a lot safer on the turbo. Also is there a mechaincal advatage to having lower compression. I figured if the pressure in side the cylinders at the point of ignition on the example I stated recently are equal to one another then why is lower compression set up more popular?