Supposedly Sir Arthur Eddington said this, and supposedly he was at least partially joking. I like to think he was only half joking, though, because there’s a pretty big nugget of truth in this supposedly backwards statement. It’s really just an obnoxious way of stating another favorite adage of scientists: Extraordinary claims require extraordinary evidence.
If someone tells you the result of an experiment, and that result fits nicely in with a previously-established theoretical framework, you should be more inclined to believe it than you would be for a claim that does not fit into such a framework. In so doing, you’re just being a good Bayesian reasoner, taking into account both your prior knowledge and the information contained in the new experiment.
Take, for instance, the idea that cell phones cause cancer. Maine is considering a law requiring warning labels to this effect. The epidemiological evidence is, to say the least, mixed. I find the “don’t believe an experiment until it’s confirmed by a theory” maxim to be a pretty convincing argument against the idea tha there’s any risk: as far as I know, no one has proposed a plausible mechanism by which the microwave radiation emitted by cell phones could cause cancer. As Bob Park has been pointing out in his What’s New column for quite a while now,
Cancer agents break chemical bonds, creating mutant strands of DNA. Microwave photons cannot break chemical bonds.
I’m terribly ignorant about biology, so maybe this argument is all wrong, but it sounds convincing to me.