We simulate ballistic deposition with long range temporally correlated noise of bounded amplitude in 1 + 1 dimension. Good agreement with the dynamical renormalization group calculation of Medina et al. is obtained for the scaling exponents when the noise is generated by a version of Mandelbrot's fast fractional Gaussian noise (ffGn) generator. However, using either the original ffGn or a chaotic map generator, other exponents are obtained. We suggest that this difference is due to an extraordinarily slow crossover caused by the existence of an anomalous growth mode incompatible with the KPZ equation. This may have implications on similar model dependent results for recent simulations on growth with power-law noise and spatially correlated noise.