That being said, there are things that you can do with a DSLR that you can't do with a P&S, but if all you care about is picture quality and not fancy features, there are plenty if P&S cameras that will work well.
My experience is a bit of the opposite. There are many mid-priced P&S cameras that are all about the bells and whistles. Lots of fancy features, like panorama modes, gps tagging, etc. But for strict image quality, you generally can't beat a dSLR. According to the DXOmark analysis, there are only a handful of P&S cameras that can come close to dSLRs.
It's the simple physics of sensor size -- the tiny sensors in P&S can't produce the same image quality of the larger sensors found in dSLRs.
Now, it depends on how challenging the situation is. Still images, in good light -- there are plenty of mid range P&S cameras that can do quite well. But say, capturing images on Disney's Peter Pan ride? Not many P&S cameras can do that.