The maximum likelihood estimator of nonlinear panel data models with fixed effects is asymptotically biased under rectangular-array asymptotics. The literature has devoted substantial effort to devising methods to correct the maximum-likelihood estimator for its bias as a means to salvage standard inferential procedures. We show that the (recursive, parametric) bootstrap replicates the distribution of the (uncorrected) maximum-likelihood estimator in large samples. This justifies the use of confidence sets constructed via conventional bootstrap methods. No adjustment for the presence of bias needs to be made.