"MARS is a nonparametric regression procedure that makes no assumption about the underlying functional relationship between the dependent and [explanatory] variables."

Strictly, this is impossible. Nonparametric or semiparametric means that we have infinitely many parameters. Hence, whenever we're fitting a non/semiparametric model using finite data set, we are forced to assume some a priori smoothness or at least continuity (here "splines") in order to achieve anything.