The 12/12 FAQ makes it clear (MH, page 42) that an Environment Mythos card triggers a King in Yellow Acts card even if it is discarded and another card is drawn. This means that Jacqueline Fine's "Precognition" ability will not prevent such a card from acting as a trigger.
However, it's also clear from the MH rules that the original 6 Headline cards from KiY that trigger Acts cards are to be kept in the Mythos deck. So, can "Precognition" still get rid of one of these cards without an Acts card being triggered? I can see arguments for both yes and no; just wondering how other people feel about it.