This is one of the most elegant examples of taking a statement out of context to reverse its meaning.
Paul Offit is a pediatrician specializing in infectious diseases, vaccines, immunology, and virology. He is the co-inventor of a rotavirus vaccine. As such, antivaxxers like to point out that he profits from vaccines. It's a strange allegation to point out that someone is paid money for doing their job, but what is more surprising is this supposed admission by Offit, not that the MMR vaccine causes autism, but:
You can never really say 'MMR doesn’t cause autism,' but frankly when you get in front of the media, you better get used to saying it. Because otherwise people hear a door being left open, when a door shouldn't be left open.
Sounds pretty damning until you realize how unusual it is to start the clip mid-sentence and swiftly end it after two and a half seconds.
Here's the full clip where Offit begins his though at around 23 minutes in, revealing the full context. Here's the transcript starting at 22 minutes
Schaffner: If you put all the studies together, would you feel uncomfortable if I or anyone else said 'you know, by now I'm very certain that vaccines aren't associated with autism...vaccines don't cause autism'?
Caplan: No, I think the evidence supports the claim...No, and I'd say the burden is now on those who want to show the connection to come up with evidence rather than conversely where good efforts have been made again and again and again with no connection. So, no it wouldn't bother me and I think in the battle in the public arena, this isn't a fight about statistical significance, it's a fight about who's going to capture the ears of the doubters and the hesitaters and I think in that war, one has to say not just 'the bulk of the evidence,' the 'preponderance of the evidence.' I think you have to say, 'there's no link!'
Offit: You know, that's exactly the analysis point. It's the right one. In the scientific method, you formulate a hypothesis and that hypothesis is the null hypothesis. You can either reject it or not reject it, you can't accept it which is to say you can never prove never. You can never really say 'MMR doesn’t cause autism,' but frankly when you get in front of the media, you better get used to saying it. Because otherwise people hear a door being left open, when a door shouldn't be left open.
This is the point at which the antivaxxer's edit ends, conveniently before Caplan interjects with
Caplan: I mean, you can never say Coca Cola doesn't cause autism!
One of the first things you'll learn in any basic statistics course is exactly what Offit is referencing here. It's also what makes science so beautiful because the evidence defends the truth for you.
We cannot prove negative in science, because there is nothing to objectively show that nothing is there. This is what Offit refers to as the null hypothesis.
A hypothesis would be a statement like "smoking causes lung cancer." This can be accepted by establishing controls and isolating only the difference of smoking or not smoking between two large groups. If we see a statistically significant difference in the amount of lung cancer in the smoker's group (and boy do we), the hypothesis is supported by the evidence and the hypothesis is accepted.
A null hypothesis is the negated hypothesis. We can reject the null hypothesis "smoking doesn't cause lung cancer" because we just showed that it does. But can you prove that playing checkers doesn't cause lung cancer? It doesn't matter how much data or controls you establish because (since checkers probably doesn't cause lung cancer) you'll perpetually end up with an absence of data to reject the null hypothesis. So we fail to reject the null hypothesis.