Matt Newman responded to my email for clarification:
With regard to the statement that a player "declares his or her intent" during the pre-initiation phase:
This sentence should be taken to mean “declares his or her intent to play the card or initiate the ability.” You are not required to choose targets or declare what you wish to do with the card or effect at that time.
As long as the card has the potential to change the game state, you can begin the initiation sequence. Then, if an attack of opportunity is triggered and that changes the way you want the card’s effect to be resolved, so be it! That is perfectly legal.
So in your example, if you play Emergency Aid and an attack of opportunity deals damage to your Guard Dog, you can then use Emergency Aid’s effect to heal the Guard Dog. You are able to do this because Emergency Aid *did* have the potential game state before the attack of opportunity occurred (because Morgan was damaged). If, hypothetically speaking, no characters in play were damaged at the time you began playing Emergency Aid, then it would have no potential to change the game state and it would immediately abort the process before the card is even played.
The same is true if you, for example, used A Chance Encounter to bring an ally back from your discard pile, and triggered an attack of opportunity that ended up defeating a different ally; you could then use A Chance Encounter to bring that ally back instead of the original one.