This was first discovered during one of Rallis's runs at 6:41 in the video linked at the bottom, where Piglet's "Flood Story" ends immediately. I have finally figured out what caused this.

In the previous board (Pooh & Honey, pt.2), you're given 18 turns to land on all the starred spaces. Rallis landed on the final star on exactly the 18th turn, which beats the minigame but also appears to set a flag to play the "losing cutscene" at the next opportunity. Going to Piglet's "Flood Story" causes it to play the losing cutscene immediately without rolling any dice. Going to one of the free boards that unlocks additional paths causes the game to glitch out like crazy and eventually reset. Trying this with other turn-dependent boards (Birthday and Rabbit's Plan, pt.1) does not work for whatever reason.

So which method is faster? After TASing both, I found that Flood Story skip turned out to be 18 seconds slower; and that's when both scenarios are played optimally. A real-time run will not be perfect, so it'll ultimately be up to the runner's discretion as to whether enough time was lost in the Pooh & Honey pt.2 board to warrant going for Flood Story skip. Remember though that you must beat the minigame EXACTLY on the 18th turn so it is risky to go for. Also note that the game does not count landing on a star as a turn, so be sure to actually count out 20 turns if trying this intentionally.