Yes, that is the case in perturbation solutions, because here you impose the transversality condition at infinity. In that case, the only solution not causing debt to explode is to inflate it away. But in perfect foresight, you are solving a two boundary problem. You are solving for a for an intermediate path for the variables satisfying an initial and terminal condition. The thing with perfect foresight simulations is that the debt equation is purely backward looking. It will simply explode and there is no way to impose that it is not allowed to explode.