If this is incorrect, please explain how it actually works, and ignore my next question 
It is no longer correct, but had been a previous interpretation that was valid per the wording of Heal. When we clarified Heal, we updated the wording and moved text around to make things clearer and give the current rules regarding Heal. The only clarification regarding battle is that you must still play them in battle per normal rules regarding the playing of enhancements (and not whenever you want as in Prep or Discard). It functions no different regardless of phase.
If a character was discarded earlier in the turn, a healability must be able to target or be played on that character as it existed prior to being discarded (the character type and brigade it had prior to being discarded), not as it is at face value in discard pile. When it is healed, it moves to its owner’s territory and regains any abilities or effects that were lost upon returning to face value in the discard pile. Any cards that had been placed on or held by a character when it was discarded are returned as previously placed on or held by the character being healed.
When a character is healed, it is no longer poisoned, diseased, or paralyzed. Any ongoing effects tied to any of those conditions end immediately.
When a character is healed, any decrease of the character’s abilities is removed.
Healabilities target the characters that are to be healed.
That first paragraph, with the bold, is regarding characters discarded during that turn, not all heal. It tells you specifically what to do with "it" (being the character discarded earlier in the turn).
The rest of the ability (underlined) describes what happens to all targets of heal (who must be "healable," per the default targeting).
So characters do not just get placed in territory because they get healed, unless it is because they are being pulled from discard.
