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.