A properly designed, well powered, double blind randomized controlled trial does a much better job at establishing causation than a retrospective correlation study, though.

"The effects of high-dose cyanide on mortality in lab mice" will establish a very strong correlation, with an impressive effect size.

I suppose inferring causality still requires a leap of faith...

Really? So atomic bombs explode when we set them off just by coincidence? Penicillin just happens to be administered every time the body decides to start fighting a bacterial infection?

That's utter nonsense. Of course they can. And they often do. Studies have limitations usually based on the statistics as a result of the size of the group and the degree to which confounding factors can be ruled out. But it is perfectly possible to establish a causative link by doing a well designed study, possibly even with small sample size.

Maybe you meant "no observational study"?