The science: It is true that when you burn any organic material it produces Polycyclic Aromatic Hydrocarbons. Wood, charcoal, meat, fat, pretty much anything that has to do with barbecue. Some of these compounds do cause tumors in mice and rats when fed at extremely high doses. The most carcinogenic of these compounds is Benzo(a)pyrene (BaP). When fed at artificially elevated dose rates of >40-45ppm/diet for about six months, a statistical difference in tumors from the control (healthy subjects not fed BaP) was noted when testing on mice.
The reality: A typical well done quarter pound flame grilled burger contains upwards of .004ppm (tested quantity) for a total of 400 ng of BaP accounting for fat weight loss. This is 10,000 times less concentrated than what was fed to the mice. Let’s recreate the lab mice test using fire grilled hamburger containing .004ppm as the food and humans as the test subjects. If all you ate was 1 flame grilled burger per day for the duration of the test, it would have to weigh approximately 2,200 lbs. I don't think you would die of cancer from the benzo(a)pyrene. There is a link between eating meat and colon cancer, but this is probably due to the lack of quality fiber in the diet.