In this case we can be reasonably confident in the causal link between the switch and the light because we're controlling the switch ourselves -- this helps us eliminate the other causal possibilities (a) that the light going on and off causes the switch to flip and (b) both the light and the flipping of the switch are separately caused by some third factor of which we're ignorant.

In situations where we can't freely vary any of the parameters we're always going to have a lot more difficulty. Given a pile of correlations between, say, happiness and the countless other variables in the mere two hundred or so countries which exist (eg "average bovine thigh circumference"), it'd be impossible, in the absence of any good theories about what should make people happy, to determine what does make people happy.

Luckily we have pretty good ideas from our own observations and from those of others about what actually does make people happy: health, wealth, nice weather, absence of civil war, et cetera. But we'll never be able to get anything other than the vaguest confirmation of what we already believed out of statistical methods alone.