In the story shown, we learn that 'everyone says it's incredible' that a mother born on Feb 29 should have a child also born on leap year day.
But if the journo could have just taken a moment to think, he or she could have put this into useful context. It certainly seems incredible if you misapply statistics and think there's a 1 in 1,461 chance of the mother being born on Feb 29, and similarly for a totally randomly occurring baby, making it a 1 in 2.13 million chance of the double. But that's just wrong because it's telling us about the chances of a randomly picked baby being in this situation, not the chances of the situation occurring this Feb 29th.
About 700,000 babies will be born in the UK this year, so with a 1 in 1,461 chance of the mother being born on Feb 29th, around 479 of this year's babies should be born to leap year day mothers. Of these, we'd expect one or two to be born on Feb 29th. Not that remarkable, then. (In practice things are a little more complex, as more babies are born at certain times, etc., but it's roughly right.)
There is always the 'unweaving the rainbow' argument aimed at Newton. Those who take this position argue that the facts get in the way of the poetry of the story. But I would argue it's possible to still find the story interesting, while being better informed by the context. Journalists would never tell us a political story without context - it's a shame (possibly because they don't know how to) that they ignore it in a statistical story.