He is a public figure, and by choice.
And not just a choice like "he plays professional baseball" but a choice like "I'm posting pictures of myself and my fiancee on Twitter, down to what suits are being worn, etc etc etc."
I think there are many many baseball players whose private lives remain private, including many of the best players of all time. Does Ryan Zimmerman have kids? I have no idea. But I guarantee that with Bryce, YOU'D KNOW.
It's the same kind of real choice he makes when he wears PEDs shirts, or things like that. If you're drawing attention to yourself in the media, you can't cry "private life" when things like this happen. If you conduct yourself privately, I think you have that right, and furthermore I think that right is largely respected by reporters.