0 definitely should be the minimum damage in ASB, not 1. You need to remember that in-game, 1 HP minimum damage when compared to the max HP on a Pokemon of 404 (base 100's +252 EVs) is only 0.25% of their HP dealt in damage to them. Percent-wise, that doesn't even register on the HP bar. In ASB, 1/100 is 1%, which is 4x larger and can make a sizable difference. An attack should be nullified completely in ASB with appropriate protection.
Of course, since this is not yet codified anywhere, it is currently up to referee discretion.