Yes, in English "he has the staircase" is not something anyone would say but that is not what this sentence means. While escalera could mean "stairs" or "staircase," the correct sentence is "he has the ladder," and the reason for this is context. Almost all of Spanish, and almost any other language for that matter, is contextual. You can see these context clues being put into effect when I say the sentence "Yo hago la cama." The correct translation of this sentence is "I make the bed," and not "I do the bed," even though hacer means "to make" and "to do." The pure reason for it not meaning do in this sentence is because context tells otherwise, and that is why in this sentence, "escalera" means ladder, because using general knowledge, with the exception of hellocma's situation, one cannot have a staircase, but they can have a ladder.
Actually, the other day my brother did have the staircase. We were putting damp proofing in the basement and we went to dismantle the staircase to get full access to the wall it was touching. Surprisingly to us, it was only fixed in with two bolts and the whole staircase moved away from the wall as a unit.