Cylinder pressure is the magic number that determines pump gas compatibility. Most conversations and articles I've seen say 180 psi is the edge of pump premium. However, like CP alluded to, cam timing is a part of it. As is piston quench, ignition timing, tumble and swirl of the charge, operating altitude, and octane.
It is entirely possible to build a 9:1 engine that detonates more than a 12:1 engine based on the above factors. The manufacturers claim of compression is just the parking lot, of the ball park, of pump gas and compression ratios. For example, the KB190 pistons in my small block can be as high as 11.8:1, but in my application with my cam at my altitude, they only have 110 psi of cranking compression, or a dynamic compression ratio of around 7.5:1.
Check this site out. It is targeted at motorcycles, but 4 stroke engines are pretty much the same. The results can be shocking.
http://www.rbracing-rsr.com/comprAdvHD.htm
