During playthrough, I'm noticing that the monsters do not have the veteran ability added into their difficulty at all. The specific wording on cards are "The difficulty to defeat is increased by the scenario's adventure deck number."
Cards that have this condition:
Henchmen: Bandit (B), Zombie Minion (2)
Monster: Enchanter (B), Mercenary (B), Scout (B), Sneak (B), Warlord (B)
Barriers: Ambush (B), Collapsed Ceiling (B), Explosive Runes (B), Large Chest (B), Locked Stone Door (2).
If need be, I can include some screen shots, but it'll be later on once I get home.