I generally think that when someone acknowledges they’ve made a mistake, or works to adjust their perspective when presented with better facts, they become more trustworthy than they were before, not less. I think they also become more human in my eyes, if that makes sense. If I were the person who believed the clickbait article, and someone told me that its claims weren’t true, I’d simply thank them for pointing that out, be glad I hadn’t been mistaken for longer than I had, and make sure to research more the next time.