the question is about situation when my character with rabbit's foot attached commits to story, may i use Jamie's Winthrop response?

keaSanya said:

I asked Damon specifically about this. In order to trigger from "draw" (like Jamie), the card has to specify the term "draw". So Rabbit's Foot does not draw a card.

Just like sacrifice and destroy end up with the exact same result they are different from a game terminology, and so different cards may trigger form one but not the other.