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.
Basen on this viewtopic.php?f=59&t=61216&p=782269&hilit=Jade+Champion#p782269 and this viewtopic.php?f=59&t=61167&p=781673&hilit=Jade+Champion#p781673
If Test of the Jade Champion resolves and I have a kiho in my hand can I choose not to discard it? I don't see why I couldn't hold the card in my hand...
Starting on your left, each player may target one of his Shugenja Personalities, then discard a card. If one player has the highest total of his Shugenja’s Chi and card’s Focus Value, he gains 3 Honor, and the Shugenja permanently gains Jade Champion and the trait, “Once per turn, when this Personality performs a Kiho action: Waive any cost of bowing him.”
If you choose to target one of your Shugenja Personalities, then you must discard a card too, unless your hand is empty. As Zen answered to this question that you found: "Targeting is optional, but if you do, you must discard if possible."
If you have only one card left in your hand and you don't want to discard it, you must choose not to target one of your Shugenja Personalities but of course you will not gain 3 Honor from Test of the Jade Champion because the total of your Shugenja's Chi and card's Focus Value is treated as zero and your opponents cannot have a lower total.