http://boston.cbslocal.com/2014/06/13/mom-flight-attendant-refused-bathroom-access-3-year-old-forced-to-urinate-in-seat/ First, I probably would have diapered a three year old on a flight or gone with pull ups for exactly that scenario. Second, oh gosh, a three year old peed herself. She'll be forever damaged and scarred....
Here's the problem. Once the airplane is at the point where they are cruising around the tarmac, no, they can't let one person up to pee. Because once they let one, then EVERYONE will get up. And three year olds can and will pee every fifteen minutes if allowed. With a slightly older child, I would feel more outrage but three year olds aren't normally considered reliably trained.