The ambiguity is partly a result of the limited space available in one-page games and partly because I think leaving room for interpretation makes story games more flexible. Ultimately the two players are the arbiters of the experience they're going to have and the stories they're going to tell, so I'm okay with the rules not always being fully explicit about what my intention is. This is one case where I think the ambiguity makes the game better, so I am reluctant to give an "official ruling."
Yours feels like a very straightforward interpretation of the game's language, though!