A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
Reads: "Reaction: Before a Personality is destroyed by a battle resolution or for losing a duel: He is completely humiliated. Negate the destruction. Dishonor him. While he remains in play, he can not be rehonored, can not commit seppukku except from a card’s effect, and his controller loses 1 Honor after each of his Dynasty Phases begins."
Whether I play this card on my own or another player's personality, would the battle's winner gain honor for his destruction?
Whether I play (Uteer Defeat) on my own or another player's personality, would the battle's winner gain honor for his destruction?
No.
You gain honor only for things you actually destroy. The Personality was not destroyed, because destruction was negated (card text).