Increasingly complex likelihood-based methods are being developed to infer biogeographic history. The results of these methods are highly dependent on the underlying model which should be appropriate for the scenario under investigation. Our example concerns the dispersal among the southern continents of the grass subfamily Danthonioideae (Poaceae). We infer ancestral areas and dispersals using likelihood-based Bayesian methods and show the results to be indecisive (reversible-jump Markov chain Monte Carlo; RJ-MCMC) or contradictory (continuous-time Markov chain with Bayesian stochastic search variable selection; BSSVS) compared to those obtained under Fitch parsimony (FP), in which the number of dispersals is minimised. The RJ-MCMC and BSSVS results differed because of the differing (and not equally appropriate) treatments of model uncertainty under these methods. Such uncertainty may be unavoidable when attempting to infer a complex likelihood model with limited data, but we show with simulated data that it is not necessarily a meaningful reflection of the credibility of a result. At higher overall rates of dispersal FP does become increasingly inaccurate. However, at and below the rate observed in Danthonioideae multiple dispersals along branches are not observed and the correct root state can be inferred reliably. Under these conditions parsimony is a more appropriate model.