Tire remnants all over my car...how do I clean them off?

Early yesterday morning, while traveling on the I-469 at 65 mph, a tire "blew" and virtually was stripped from my Ford Taurus like someone was peeling an orange. Pieces of the tire flew everywhere, damaging the underside of the car and also marring the rear quarter panel with 'remnants' of rubber all over the car's body. How can I remove this without damaging the paint?

The motor club tow truck driver, my mechanic, and a local tire dealer all told me (independently) that Ford intentionally put cheap Continental tires on the '02 Taurus models, and that the tires have a history of exploding. The car only has 42,000 miles on it, and - until this damage - was in perfect condition. Will rubbing compound take the black marks off? Or should I take it to a professional body shop or auto detailer? Thanks in advance for any worthwhile advice!