I think this is probably true for some people, the same sort of person who sees something on Facebook and assumes that it's true. [1] But there are quite a lot of people for whom "according to whom?" is the next question after being told something factual. For them, I think search's job is to find relevant sources and get out of the way.
But I think even finding out is a long way away. The main thing that ChatGPT has nailed is glibness. It produces text that sounds authoritative, whether or not it's correct. And it's often incorrect. People may try ChatGPT search out of novelty or because it feels human. But if they depend on it and feel the real-world impact of a confidently wrong answer, they're going to treat it as a human that's untrustworthy. A blowhard, a liar, a fool. So I'm sure the major search players are going to be very cautious rolling out chat-like things. Google has spent decades building up consumer trust, and the don't need a zillion articles about people who a too-confident chat steered wrong.
[1] E.g., That men in white vans are kidnappers: vhttps://www.cnn.com/2019/12/04/tech/facebook-white-vans/inde...