They say x, ask for where they heard about x. They say from y news organization, ask the source for y. If they say z, if z is actually an actual document or otherwise, ask them where in z does y claim x is true.
If z is just another news organization, keep going until they provide (or don't provide) an actual document. If they can't procure an actual document, send it yourself. If z is just another video cIip, ask them for the whole video. Provide them the entire video if they can't.
Do not try to antagonize. Just simply ask the questions as if you were trying to understand their point of view, to learn something we might not have heard.
Here's what I do:
Me- I really want to make sure I have both sides correct in any situation. So, I will tell you why I think you don't like Donald Trump. No snark or sarcasm allowed.
Then you tell me why I do support him without snark or sarcasm.
That is the point. It is to point out that they haven't actually "thought" through anything. If you asked me why I don't support Obama, I could give you many issues that that Obama championed that were detrimental to Americans, without name calling him. They can't do that. That is the point they need to realize. Also, I have used this many times, but not to strangers, but rather people I know.
The one issue I always tag with Obama is the fact that he funded and continued to fund ISIS while they were mass slaughtering Christians, half a million of them.