No, it does make a difference to have more information and especially more incisive and clear facts that are easy to present.
I haven't had many arguments about Hitler's death, but I've pulled people away from the moon landing conspiracy theory, and a bunch of others. My success rate got much better once I was able to walk them through the Apollo 11 mirror and the detection of it from earth. It's not perfect, but it makes a difference having a single clear piece of information you can offer them, especially one they hadn't considered before.
Consider different types of conspiracy theorists:
1. Ones who copy something they vaguely heard. New information is a relief to them. They don't like being on the outside. Even if you are only temporarily their new source of authority, convincing them of the truth is a win and you can build from there. Also, you can usually find someone they regard as an authority who can present the information.
2. Ones who want to have inside/obscure knowledge of something. Telling them a fact most people don't know is exciting. They may switch to the truth just to have one up over their fellow theorists. They may become your best research partner.
3. Ones who have put in work to adopt conspiracy theories but are genuinely confused about the story. These can be won over with an abundance of factual information and analysis. So not only do you mention the dental records, you show them the whole paper, review the other pieces of evidence, etc. They take time but the effort genuinely pays off, likely for life.
4. Ones who think anyone but their unhealthy brain or true cult leader is trying to deceive them. You probably can't win here. But they're far from most common and you generally know if you have one of these on your hands.