How do we know that these solutions don't exist in the training data? It is open secret that they have used pirated materials for training. Perhaps it plagiarized solutions from works of some obscure Belgian mathematician from the sixties, who did not get mainstream acceptance. I wouldn't be surprised if they also got access to mathematics done in the "defense contractor" setting from various three letter agencies.

Without a searchable index of training data, it is hard to put faith into these claims.

This wouldn't be a problem so long as they properly attribute.