Seriously Sinky, I am not blowing smoke up the pant leg here. I really do remember it being in the news, on TV. No I don't believe I am confused. I'll do some searching myself, maybe an old News Paper, Printed Copy would be the way to go. I'll check the newspaper archives. I am really serious, no joke!!
OK. If you find something, from a credible source, I'll retract. But I've checked every search engine I know of, and there's not a single hit on "Montini illegitimate child" or "Paul VI illegitimate child."