Although it doesn't explain everything (her fingers of doom in "Q Who", for example), I figured Guinan's paranormal abilities came from her time in the Nexus. When you're connected to a place where time has no meaning, you're gonna sense when the timeline changes and timeless-you suddenly won't be making those Picard/Kirk introductions.
(I suspect they originally planned for Guinan to have Q powers herself, but chose never to use them. Then someone probably realized that once the secret was blown she'd have to leave the ship for any further episodes to have any peril. That, or she was a Time Lord.)
She was not very happy when the timeline was altered in YE, and I doubt she'd have let something big slip by like sending the wrong ship into the past.