The ability of radiation to cause cancer is dependent on whether or not the radiation is able to alter chemical bonds. This occurs when electrons involved in bonding in a molecule absorb radiation with enough energy to allow them to escape – this is called ionization. The thing is, whether or not radiation is ionizing is based solely on its energy, not on its number, and as we saw above, its energy is determined entirely from its frequency.
Cool article on WordPress.com about Why Cell Phones Can’t Cause Cancer, But Bananas Can, which I read while eating (and finishing) a banana. It covers dielectric heating too.