I believe that they are, indeed, referring primarily to the penalties, which means that, for a turn, you act as if you have no injuries. If you're playing with the optional rule that the damage penalties also apply a penalty to your defense or attack rolls, you'd ignore the penalties there too.
I wouldn't allow it to bypass Death or Unconscious. I'd probably allow it in a Dying case, albeit only for a single Move or Standard action (it fits nicely with the genre for the hero/villain to pop up and make one last attack whether it's the grizzled detective firing off that last shot to blow up the kingpin's escape vehicle, the seemingly dead victim who grabs the killer's leg, or the revenant slasher who pops up for One Final Attack on the Last Girl. And it would probably allow you to bypass the Staggered/Disabled penalties of only a single action.
Personally, I think it's a rather underpowered advantage, but I can see its uses.