The crucial part here is how big is the gap between a proposee’s worst and best match: if the gap is null for all proposees, there isn’t any strategic incentive for one to lie about their preferences. However, that obviously is a very hard requirement.
There's a variant where you run the deferred acceptance algorithm, but then only the proposees who never rejected anyone finalize their decision. All other proposees and their matched proposers split up, and the whole algorithm is run again with the unmatched participants. This time, you end up with a Pareto-optimal matching for the proposers, with respect to their stated preferences. That is, there's no possible way to make anyone happier without making someone else less happy. But it's not stable, and the algorithm is no longer strategy-proof. (In fact, one can prove that no strategy-proof algorithm can guarantee a Pareto-optimal matching!)