I think it should be incredibly easy to verify this. Just look at the training data and see if it contains any of the chats. It should be trivial for a company with tens of thousands of super-genius agents at their disposal.
Just because something is in the training data, doesn't mean it is the root of an LLMs output.
Turn off web search and ask a model what a random redditor said about a random topic in 2015. You will only get hallucinations at best, even though that comment is definitely in the training set.
What they're saying, and I think this was the clear implication of the blog post too, is that the training data definitely would contain these chats and the only question is whether it got encoded into the weights.
Two steps would be needed.
(1) We'd have to identify their chats. How would we do this? We'd need them to share their chats with us so we could look for matches.
(2) We'd have to prove those chats changed model behavior. How would we do this? We'd need to retrain many models with those specific chats removed, and ask those models to solve the Navier-Stokes problem many times, and keep doing this until reaching the desired level of statistical significance.
#1 requires their cooperation and a bit of work on our side. #2 is extremely expensive and not really feasible.