Okay, so "January Jones Birthed Her Bastard" is not the most sensitive headline in the world. But the headline is, dare we say it, on to something — in a world where out-of-wedlock births are increasingly common, there's no term for a child born to unmarried parents that doesn't sound totally weird.
At one extreme, we have "love child." This implies that the baby's parents were in love, which isn't always the case, and it also kind of implies that married parents aren't. Presumably left over from the days when marriage was for economics and cheating was for love and lust, this term still gets used a lot in tabloids and elsewhere ... mostly because the alternative is "bastard." Which is unprintable in some contexts, and offensive, and also makes you sound like Dickens. What's a polite person who wants to describe the fruits of a non-legally-sanctioned union to do?
Of course, you can say "fruits of a non-legally-sanctioned union." Or "child born to unmarried parents." Or make up your own word (suggestions?). But really, the only decent alternative I can think of is one that acknowledges that, especially in a country where not everybody who wants to can legally get married, the marital status of one's parents isn't really all that important — maybe we should just call each child a child.
January Jones Birthed Her Bastard [The Superficial]