EDIT: (In response to Zen's request to find him a non-hypothetical example)
Yoritomo Harada
Recon Open: During battles at a target province this turn, you have the ability: "Reaction: Any number of times per turn, after one of your Personalities is destroyed: Target an attachment destroyed with him. Attach it to a target Personality in your current army (paying all costs)."
His ability allows me to move all of the attachments on a destroyed personality, according to viewtopic.php?f=59&t=60761
Yes. Although "A player can not use the same Reaction or triggered trait twice to a single triggering occurrence from the same copy of a card, or from the rules," (http://rules.l5r.com/Timing), it is written under the assumption that the action is only usable once per turn.
This particular rule has been around from the time that Reactions without a once-per-turn sort of cost were printed. It was to prevent cards such as Naka Kuro Experienced (Reaction: When Kuro performs a kiho, draw an additional card during your next end phase.) from being abusive. I infer that the rule is newly made with Samurai Edition in mind. (I stopped searching once I reached this first example. I can find more)
Using a currently legal card as an example, you enable stalling during tournaments using this simple tactic with Shosuro Aroru experienced: (Reaction: Any number of times per turn, after another player's Battle action resolves: Move Aroru to any location.) I react to my opponent's Battle action by moving Aroru home, then I react to the same action by moving Aroru to a battlefield, I then react by moving Aroru home, I then react by moving Aroru to a battlefield, ad infinitum.
While the above situation is not helpful to a player, it is a situation disliked by judges.
After a search for Lotus-legal cards (those that are normally once-per-turn) Tsuruchi Futoshi came up. Reaction: Any number of times per turn, after another player draws a card from his own card effects: Ranged 3 Attack. If this is the Action Phase, this can target cards in players' homes.
One card drawn during the Action phase equates to death of all personalities the opponent owns with force 3 or less that have no 4F followers attached.
I am certain that "A player can not use the same Reaction or triggered trait twice to a single triggering occurrence from the same copy of a card, or from the rules" is designed to prevent [edit]this kind[/edit] of situation from happening, not simply to serve as a reminder of the Once Per Turn rule.