You didn't say if the low profiles were also run flats but I'm assuming they are since it's a new car. Yes, low profile run flat tires are subject to blowouts, especially when hitting a pot hole! I had two blowouts within 2000 miles in my new 2008 GS460. Someone in the club suggested I buy new tires without the run flat feature which would also provide a much smoother ride due to the elimination of the hard wall casing in the run flats. I bought new Michelin Pilot Sport A/S Plus tires and have had no problem since plus the ride is a lot smoother without experiencing any appreciable loss of performance.
Since the car did not come with a spare, I also spent 3 hrs convincing the dealer that a spare for my car was available and was successful in buying one.