Cards check turns during the upkeep phase. AiG works like this in regards to looking at when to discard itself.
The ruling at Nationals is that AiG only checks on turn 3. If Stoic is later negated, shuffled, discarded, etc, AiG won't check again later to discard itself. Because there was really no precedent to this type of scenario, a few of the elders who weren't involved in the event came to that unbiased ruling.
Later, when we were discussing it in a larger group, there were varying views on whether or not AiG only checks on turn 3. The ruling from Nationals still stands, but it's something that we will look into further. We need to take time to assess all turn based cards to see how they are played and apply the rule consistently across the board.