The parents, now divorced, presumably once obtained a civil license and entered upon a legal marriage. Children from that union are, therefore, their legitimate offspring. Legitimate means legal. The civil divorce and the Church annulment do not alter this situation. Nor do they change the parents responsibility toward the children. In fact, during annulment procedures the Church reminds petitioners of their moral obligation to provide for the proper upbringing of their children. Nevertheless, persons pondering the Catholic annulment process do often express this concern about the legitimacy of the children after that procedure. Its a persistent rumor.
I certainly do agree with you, though, that the annulment of a 27 year marriage, with children, is pretty fishy... like many other political annulments. Nonetheless, I have yet to see a Catholic authority stating that the children are illegitimate after an annulment. I think whether Kerry, Kennedy, et. al., should have gotten an annulment is another issue entirely and I suspect most posters on these threads would agree on that point.
Almost sounds to me like there's no sense is bothering with a 'church annulment' at all. I thought these things were almost impossible to get. Doesn't seem like they are all that difficult.