Yeah there's not a lot of clearance on these things, I have Shinko SR-007 tires which really hold the road and I've 'scraped' going around a turn quickly before... Wasn't even going that fast, I didn't think, like yourself it let me know, these are not sport bikes.
Worse still is those sorry rear shocks don't hold up much.
And you better haven't lowered your ride in favor of speed and fuel economy.
One thing I did learn is we can always use the line through technique, works way better than in a car.
http://www.lazymotorbike.eu/tips/corners/