The quote in question:
A take or give effect is permanent, unless a duration is specified. If a duration is specified, when the duration is reached the Permanent Controller List is updated.
And the PCL entry:
Permanent Controller List
While a card is under the permanent control of any player, it maintains a list of the players that have had permanent control, as well as the effect that gave that player permanent control. The first entry is always the owner, even if it was initially under the permanent control of another player. If an effect changes permanent control to a new controller (as opposed to reverting to a previous controller), it adds an entry to the end of the list. If the effect has a duration, when the duration ends, the corresponding entry is removed, and if it was the entry at the end of the list permanent control reverts to the player in the entry currently at the end of the list. If an effect specifically reverts permanent control to a previous controller, it reverts to the indicated entry and removes entries after it. If an effect specifically reverts permanent control to the owner, the list reverts to the first entry and removes all other entries.
I assume that because you can still attack with an opponent's hero (usually by banding to them), even though they have control again it doesn't kick the hero out of battle. I would assume it works the same if, say, you used Corrupt Earth to discard Nic's Teachings from a hero in battle. If it were a TC hero in a territory, they would go back, since you can't usually have an opponent-controlled character in your territory.
EDIT: not sure why the second quote isn't working.