Chances of three generations being born on the same date: I have no idea. Quite low, most likely. I’m not skillful at the statistics of probablilty. (The article says 272,910 to one; I have no reason to dispute that.)
Chances of three generations being born on the same day: nil.
It’s no wonder we cannot expect newspapers to get big stories right (or reported at all, often); we cannot even expect them to understand the language anymore.
Afterword: It’s possible this is an English-English vs. American-English usage difference. Until that is proved to me, I’m staying snarky on this one.