This article provides rigorous proofs that neither Efron's bootstrap nor permutation techniques can be applied directly to the observations to construct consistent resampling tests for transition probability matrices of finite-state Markov processes. These methods modify the covariance functions of the limiting distributions of the involved Aalen-Johansen processes, even in the case of fully observable individuals. An example for the failure of these resampling methods is given by cumulative incidence functions in competing risks set-ups.