No, it's the other way around: if you share your personal experience with me, I'll respect
you more than I would if you instead shared facts. At least, that's the authors' claim.
But what it means to "share facts" in these studies is not what you might anticipate. In Study 5, for example, participants speak with someone who disagrees with them about gun control. In the article, we're told that these interlocutors "offered either personal experiences or shared factual knowledge to support that stance." But the Supporting Information (which is separate from the article) shows what the interlocutors really said:
> Well, I do think you’re wrong about gun policy. I am [for/against] gun control, and I feel pretty strongly about that. I don’t know how you can call yourself an American if you don’t think that guns [hurt people and communities/keep our communities safe]. I believe this because I have read many books and governmental reports on gun policy, so my factual knowledge has really made me feel strongly about this. [1]
The interlocutor claims to be basing his views on "factual knowledge," but no actual facts are offered. To me, this seems a bad way to study the effects of fact-giving in discussions. If you want to do that, you should...study discussions in which facts are given.
Study 4 is similar in this respect. Then again, in the authors' defense, there's more to the article than these two studies.
[1] https://www.pnas.org/content/pnas/suppl/2021/01/25/200838911...