I also had a bad wreck once with brand new tires. The rubber was a lot harder than what I had been riding on. I took a hard left at a decent speed that I'd taken 100 times before, but with the new tires the bike just kept going straight, and I hit pavement at 20 MPH, straight into traffic. Amazingly, there was about a 200 foot gap in traffic, and I was able to grab my bike and get back off the road before any cars got to me.
I was trying to get my chain back on the chainring when I realized the stuff dripping onto the chain was blood, so I went back home and bandaged up.