This is not true. Nonlinear functions generally do not result from combinations of linear functions. It's the other way around -- combinations of linear basis functions are often used to approximate nonlinear functions, often in a spline sort of way.

However, this only works (practically) for mildly nonlinear functions. If you have exp, log, sin, cos functions for instance and you're modeling a range where the function is very nonlinear, the approximation errors often become problematic unless you use a really dense cluster of knots. For certain nonlinear systems of equations, this can blow up the size of your problem. It's a tradeoff between number of linear basis functions you use for the approximation, and the error you are willing to accept.