The source is not what’s convincing you, it’s the way the ai is presenting you the information. The source just confirms what you’re already thinking at that point (what the ai has just presented to you). You’re still trusting the ai.
That may be true of the average user, but you have no way of knowing it's true of the person you replied to. It's 100% possible to check the sources properly, and form your beliefs accordingly, if you want to.