I'm well aware that when we use the expression "linear model" we are actually making reference to models that are linear on the parameters $\beta$. And because of that any polynomial regression will be consider as linear.
Anyway I've been reading "Elements of Statistical Learning" (Hastie, et.al.) and I found a phrase that confused me a little.
Linear regression, linear discriminant analysis, logistic regression and separating hyperplanes all rely on a linear model. It is extremely unlikely that the true function f(X) is actually linear in X. In regression problems, f(X) = E(Y |X) will typically be nonlinear and nonadditive in X, and representing f(X) by a linear model is usually a convenient, and sometimes a necessary, approximation. (p.139)
He states that generally we use, for the sake of simplicity, linear models, but that it's extremely unlikely to have a true function linear in X. And because of that we could use "non linear models" (but non linear in X, like for example polynomial regression).
In my opinion it's a little bit confusing, given that generally we use the terminology "non linear models" to talk about "non linear in parameters".
Am I missing something? Is it usual to use such terminology when referring to polynomial regression?