No you don’t. You just need a package that is solving the same (nonlinear least-squares) optimization problem [*]. RAFF is solving a different “LOVO” optimization problem that generalizes least-squares by eliminating “outlier” data points, and hence will yield a different result.
[*] With the caveat that if your problem is nonconvex with multiple local minima, then different algorithms, different implementations of the “same” algorithm (e.g. different initialization strategies for Nelder–Mead), and different starting points may yield different minima. But with a suitable starting point any convergent local minimization algorithm should be able to locate the fminsearch minimum.