My gut ( :-) ) tells me that humans will continue to trust their guts in a large percentage of cases regardless of the advice they receive from other humans or from AI. Unless the AI is more successful at overcoming the long list of biases which we possess I don't see it being much more successful. If anything, it'll be easier to reject advice from an AI than from a human unless the AI is armed with some ability to coerce us into taking its advice!
As the old saying goes: "You can lead a horse to water but you can't make him drink"...