All right, I think I've figured out exactly why
No Refuge and
Troop Tower don't work when another player has a minion stacked.
When you are a Shadow player, your own Free Peoples cards don't even exist (and vice versa) as far as the game is concerned
except when they are referred to as "cards," "Shadow cards" or "Free Peoples cards."
So when your fellowship is at
Pelennor Flat, you can discard Shadow cards from your hand, because the site simply says "cards." Likewise,
Forearmed can reveal a Shadow card from the top of your deck and reduce a minion's strength based on its twilight cost.
Using this logic, it is clear that
No Refuge and
Troop Tower only work when that card's owner has minions stacked. Because
No Refuge cannot spot them as
![Dunland [Dunland]](https://lotrtcgdb.com/forums/Smileys/classic/dunland.png)
minions stacked on a site; they are only "cards" stacked on a site.