Sorry, but no. The null hypothesis is that there is no relation between two variables. You have to do experiments to estimate the probabilities of the null and alternative hypotheses. You don't get to label the one with the higher prior as the null hypothesis; that's simply not what that term means. It does indeed mean "it's not true [that A affects B]".

> If my wife said "I'm going to the shops" I wouldn't assume she was lying until proven otherwise.

I certainly hope you wouldn't! But the null hypothesis would indeed be that the words she speaks have no bearing on whether she is going shopping. I don't know your wife, but I find it easy to believe that your prior probability of that hypothesis is quite low.

(At least, until it becomes a pattern where she's regularly staying out all night with more and more flimsy excuses....)