Epidemiologists just love talking about how John Snow identified contaminated water as the way cholera is transmitted.
His most famous investigation was into an outbreak of cholera in 1854 in Soho. He found that the cases were all associated with one single water pump, in Broad Street. What further strengthened the conclusion is that it turned out some cases of cholera further away were nonetheless drinking water from the pump, and some residents close to the pump who didn't get cholera didn't drink from the pump (some of them worked in a brewery and were given free beer!) He persuaded the council to remove the pump handle.
In a previous outbreak of cholera, he had tracked down all the cases and identified whether they got their water from the company which drew its water from the Thames upstream of London or the rival company which drew its water from downstream. Not surprisingly to us now, the latter was the one producing cases of cholera.
At the time, people believed that cholera was spread through bad air - "miasma". It wasn't until 30 years later in 1885 that the cholera bacterium was discovered. So this episode is sometimes cited as evidence that you can draw conclusions about causation even if you don't know a mechanism. The implication is that we shouldn't be unduly deterred from drawing conclusions about whether magnetic fields cause cancer just because we don't know the mechanism.
There is a valid point here: yes, if the epidemiology is strong enough, you don't need a mechanism to infer causation. But there are limits to the comparison as well. First, John Snow's epidemiological evidence about cholera was very powerful indeed - epidemiologists today would give their eye teeth to find an association as clear as those hedid. And second, with magnetic fields, it's not just that we haven't found a mechanism, there are arguments that a mechanism may actually be impossible because of how weak the fields are.
The wise conclusion is that the absence of a mechanism for magnetic fields does not of itself rule out effects. But it is part of the overall weight of evidence.