Can any "model" be cross validated? Suppose you have a dataset that has heights of people and whether they play basketball professionally. You have a theory that anyone taller than 200 cm plays professional basketball and everyone shorter does not. This is your "decision rule" (i.e. model).
If you took 20% of this data and tested this theory - measured how well this decision rule predicted if someone plays professional basketball: is this a statistically valid approach to test how well this rule might "generalize" to unseen data? Then repeat this several times on random 20% subsets of the data?
Does this sound reasonable?

Yes every model can be cross validated. That is, every scientific model can be cross validated.
This relates to the theory of science of Popper about falsification. Scientific theories/models should be able to provide predictions according to which they can be tested.
From this point of view 'cross validation' is just the testing of previously established theories/models.
In the point of view/framework of statistics the 'cross validation' is a more elaborate scheme of testing different models based on the data. In a first step the unknown parameters in the theories are determined based on data (which might lead to over-fitting and might lead to the wrong idea that the theory/model works well), after that an additional cross validation step on new data is used to verify and select the best working models/theories.

So there are two requirements for models to be cross validated.

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*A requirement that models can be validated As long as the models provide testable results there can be cross-validation.

*A requirement that models need to be validated Cross validation in statistics is in particular used for the cases when models/theories contain unknown parameters that are fitted with data. This fitting makes them prone to over-fitting and cross validation is used to filter/verify/select which model/theory is best.
If there is no fitting then there is neither much use for cross validation.



is this a statistically valid approach to test how well this rule might "generalize" to unseen data?

If you mean 'does this generalize the model' in other regions, ie extrapolation, then it is not true. It only generalizes to new data from the same region (but with different noise).
Cross validation does not allow one to extrapolate. It is only working in the range from which the data is sampled.
The reason to use cross validation, and the idea about 'generalizing to unseen data' is relating to the sample being a specific case/dataset which involves different noise that won't be the same in other data sets.
So we can test/cross-validate models on different data sets with different noise, but this is not the same as allowing to extrapolate the model to other regions, instead it is allowing to "extrapolate" or generalize to other datasets (with other noise) within the same region.
The extrapolation of the model involves extrapolation of the determistic term, and that is not tested with cross validation.
