That's not even an argument. Here is one against the claims.
Modification: There have been repeatedly successful case of transfer learning where you take a pretrained deep neural network and train on a new dataset (even very small).
Vulnerability: you dont need the training dataset to test vulnerabilities, you just either very specific input (that you probably gonna have to create yourself because they are so specific that they are not even in the dataset) or using one input that you corrupt for attacking. And as far as I know it doesn't sound harder than making test for regular algorithms.