The Truth is in the Wine indeed... and based on the second panel it seems that he already knows what that Truth is (Ai-chan's clueless face is adorable though).
It's not even sake. It's amazake, which I believe the alcohol content is so insubstantial, even kids can drink it safely.
The "Wait, no!" gesture from the dude in panel 2 suggests that he was expecting this result. Either they got some real sake in there by mistake, or Jitome-chan has some sort of alcohol intolerance (which the head priest knew about but Ai-chan did not) which makes her able to get drunk on amazake.