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I would say it's about the effect, not the action. From the rulebook, section 3 Minion phase, Bleed, this is how successful bleed is defined:

Effect: If the action succeeds, the target Methuselah burns an amount of pool equal to the bleed amount. By default, all vampires have a bleed amount of 1. If the action succeeds and the bleed amount is 1 or more, then the bleed is successful and the controller of the acting minion gets the Edge, taking it from the Methuselah who has it, if any.