Actually my wife and I were at St Peters Basilica this summer as well. As one of the other poster's mentioned you can just turn the flash off. This worked great for us. We had a Canon Power Shot 200 I think (it was 2 mega pixel, I get mixed up with the different model numbers.)
My question and slightly off topic is how to get the same pictures to turn out with a 35mm camera. We had both and all of the digital pictures were great and the 35mm were a bust. I suppose a slower speed film would help (I think we were using 200) but we didn't have a tripod so keeping the camera still would be hard. Am I missing something nice and simple?