Earlier quoted context omitted.
The simple idea is to do stuff like train your model on randomized subsets of your data and then compare its performance to using all the data you have. This doesn't overcome a true "black swan", but that's not what NN are meant to be doing anyhow.
"The simple idea is to do stuff like train your model on randomized subsets of your data and then compare its performance to using all the data you have." How do you do this when you cannot verify that your data, in subset or in whole, is accurate? And furthermore you don't know how inaccurate it is?
If you have no idea of the accuracy of any of your data then you're probably asking the wrong question of it. You can do things like test for consistency using cross-validation, e.g. does half of your dataset predict the other half with the same kind of performance? But that can't detect the same errors repeated throughout your data.