Keep in mind this is the same concept as is used in MRI. If MRIs were causing cancer, I think they'd be a lot less popular as a diagnostic tool.
There may be epidemiological validity to findings of higher rates of certain cancers among populations living near power lines, but that doesn't mean the power lines are the causation. Usually, because power lines are unsightly, they are undesirable locations for homes, and therefore the property values much lower near them. There are a lot of risk factors associated with low SES, including things like worse healthcare, more common tobacco and alcohol abuse, occupational exposures at blue collar jobs, more obesity, etc.