Pros and cons of cross-validation? A practicing statistician I know advocates strongly against cross-validation, claiming that he would rather build the model on the entire dataset and make sure the underlying statistical assumptions are rock solid, as opposed to cross-validating his models. With solid statistical foundations, he argues the models should predict well out-of-sample.
What are your arguments for or against cross-validation?
 A: 
With solid statistical foundations, he argues the models should predict well out-of-sample.

Assuming that by "the underlying statistical assumptions are rock-solid" and "solid statistical foundations" he means "accurate assumptions", this is wrong. Models with more accurate assumptions may make worse out-of-sample predictions. Domingos and Pazzani (1997) has an example of this: even with simulated data generated from a known, complex model, a simpler model can perform better than the true model.
Domingos, P., & Pazzani, M. (1997). On the optimality of the simple Bayesian classifier under zero-one loss. Machine Learning, 29, 103–130. doi:10.1023/A:1007413511361
A: 
rather build the model on the entire dataset 

That is what is usually done for cross validation (in the validation sense): the test results for the surrogate models are used as approximation for prediction of unknown cases of the model built on the entire dataset.

and make sure the underlying statistical assumptions are rock solid, 

This is (obviously) always a good idea. But it is not opposed to any kind of validation method. 

as opposed to cross-validating his models.

Here's the weird thing: both points above are not opposed to cross validation. 

So: after building the model on the entire data set and having made sure the modeling assumptions are met, how does your statistician friend validate the model?

Note that there are situations where cross validation is not a good choice, e.g. if you have multiple important confounders so you need to split independently of all of them, you end up with very small test and training set sizes for the surrogate models.
