The rules actually say the following:
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Any Treasure card may be played to the table as soon as you get it, or at any time on your own turn except during combat (unless the rules below or the card itself says otherwise).
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Most of the exceptions alluded to in further rules would be those in the "One-Shot" Treasures and Special Treasures sections.
I also want to make clear: Items received during a trade must already have been in play and must stay in play, they do not go into your hand, and since the rules explicitly say that a player in combat can't trade, there's no issue there.