From your statement, is your position: If a Fallen Wizard has played White Tree using Wizard's Trove and it's text is ignored, then a hero Wizard may play White Tree as usual since "Unique" on the first White Tree is ignored. But if the hero Wizard has played White Tree as usual, then a Fallen Wizard may not play White Tree using Wizard's Trove because the "Unique" keyword would be checked at declaration before being ignored?
Putting aside the rules, is that the way that you play? Do you know if others play that way as well?
I checked the rules again and I do not see the restriction: "If unique card has to be played, it is checked whether its copy is in play
First, looking again at the rules on keywords, I notice that keywords like Unique actually are in the card's text
. And Wizard's Trove says "ignore text", which includes keywords. It doesn't just reference the "effects" of a card, which is commonly done by other cards.
Several types of cards are referred to by the keyword included in the first few words of a card's text. For example, the text of a "spirit-magic" card starts with Magic. Spirit-magic; the text of a "wolf" card starts with Wolves; the text of a "Palantir" starts with Unique. Palantir.
Keywords do not necessarily carry any rules (though some do like Unique and Corruption). Keywords are used to determine if an effect in the game affects a card.
Then, looking at the rules on Unique they only prevent more than one Unique card from being "in play
." Being "in play" is different from being declared ("played") per Annotation 1. At resolution of Wizard's Trove, White Tree is played and "Unique" in it's card text is ignored. So I see no reason for preventing play of White Tree using Wizard's Trove even if White Tree has been played normally. Especially since Wizard's Trove says to ignore the "Unique" keyword of White Tree.
UNIQUE & "MAY NOT BE DUPLICATED" CARDS
If a card states that it is "unique" or that it "may not be duplicated,'' only one such card (or its effects) may be in play at a time. The first card played takes precedence (influence checks may change this). This restriction applies to all cards in play, i.e., both yours and your opponent's.
Only one of each "unique" card may be included in your play deck and starting cards combined. As an exception, two of the same Ringwraith may be included in your play deck (to give you a better chance of drawing one early).
Annotation 1: A card is not in play until it is resolved in its chain of effects.
A lot of Stage Cards require a "protected" Wizardhaven (one needs 2) but only Wizard's Trove and Guarded Haven can protect a Wizardhaven other than The White Towers or Isengard. Maybe this is the reason for ignoring "Unique."