This question made me think about what we know about the Xenomorphs. Namely, that they have exoskeletons. How is it the Predators have an exoskeletoned creature's inner skull in their trophy case?
We know that the Aliens have a hard exterior, but that alone does not prove that the creatures have no internal skeleton. Armadillos and tortoises sport hard body armor but also have endoskeletons. The insectile appearance of the Aliens suggests an exoskeletal structure, but scaling problems would cause a creature to collapse under its own weight unless we posit the existence of unreasonably strong materials.
So I believe the initial premise is wrong: Aliens have endoskeletons, not exoskeletons. The hard exterior is simply armor.
There's an unspoken assumption here: that creatures with an exoskeleton don't also have an endoskeleton. That may be true for creatures on Earth, but Xenomorphs did not evolve on Earth. Given their extraterrestrial origin and evolution, I think it perfectly reasonable to think that Xenomorphs could have an endoskeleton in addition to their exoskeleton.