Isn't the problem here that things are backward?

You don't prove causation, but you can disprove it when you find absence of correlation.

Observed correlation suggests causation which allows you to make a prediction. A prediction can be tested. The prediction will either be true or false based upon whether the correlation continues to hold.

This is one of the problems with A/B tests--they often don't have causation aka "Why?" "This dialog box was rearranged and gave us 15% better conversion." Um. Okay. But "Why?" If you can't answer "Why?" you don't have causation.

"We removed needing to enter a phone number and now have 15% better conversion." "Why?" is obvious in that case.