Compression ratio does NOT change. The definition of compression ration is the maximum cylinder volume divided by the minimum cylinder volume. Or expressed another way, the sum of the swept volume and the clearance volume divided by the clearance volume. In other words, it's set by the piston, cylinder head, and cranktrain geometry, it has nothing to do with the density of the air that enters the combustion chamber. The intake charge in turbocharged engines is typically hotter (due to being compressed) than in naturally-aspirated engines, and therefore more easily ignited, hence the need for higher-octane fuel. Under high boost conditions there's also a risk of running lean which also leads to knocking.

FWIW, I run my 740 Turbo on 89 octane - it doesn't knock even under WOT with Turbo+ (higher peak boost), and it gets 27 MPG on the highway over a 300 mile trip at 70 MPH. It has a manual transmission - if you have an automatic, your MPG will be lower.

Zack
1980 245DL M46 277k
1988 745T+ M46 207k