Yup, tire pressure profiles are specific to the combination of tire and car. Yes, your pressure will increase on the track. No, I've never ever seen a tire blow out on the few tracks I've run in CA and WA. What I have seen and experienced are destroyed street tires because they weren't inflated higher than standard. While you do theoretically have less contact patch the reality is you won't. We're not talking pressures that put the tread out of round. What you will find on high speed corners with lower pressures is that your tread corners are much more important than the patch and this is where you will end up missing chunks of tire down to the cord because you're rolling the tread over with lower pressures (I found this out the hard way when I destroyed a new set of PS2s with about 40 minutes of track use - once.) You need higher pressure in order to not roll the tires in the corners where they do the most work, not the straights.
For perspective, I'm talking purely about max performance summer tires, not racing compounds. Also, my tire pressure doesn't rise more than 6-7 pounds but I'm running in a cooler environment than most in WA state so if you guys are seeing 12 lb bumps I would imagine it makes sense to start lower than the numbers I mentioned - even then I can't imagine starting under 40 lbs cold.