DNA mutates spontaneously from background radiation and mutagens present in the cytoplasm (oxygen is even one!) and etc. This isn't normally a problem because the rate at which this happens is balanced by protein repair kinetics, however, if you are boiling the blood denaturing these proteins isn't an unreasonable expectation in non-thermophiles... Furthermore, if you're boiling blood, DNA can uncoil and become susceptible to other problems.
The question is what power is required affect this balanced system. Apparently over time mutations occur which cannot be repaired and sometimes after that cancer occurs ordinarily. It is easy to tell when this happens to 100% of organisms you're studying after doing X and waiting less than a year's time, but is considerably harder to answer when you're trying to see if there is a lethal effect over 60 years in 1 in 1,000 or 1 in 10,000 or 1 in 100,000 or 1 in a million. This is an open and challenging problem.
I don't claim microwaves of some power won't cause cancer, but I also won't claim oxygen can't cause less cancer. In the microwave case there isn't enough evidence to expect it in lower power situations, but to some tolerance there is always a possibility.
The problem with a lot of folks is the way in which they perceive risk. Risk management should be taught. SF should worry a lot more about an earthquake than cancer from wifi.