Stairs implies a fixed structure that cannot be carried but climbed.
You are right. In this case only "ladder" should be a valid option, although "stairs" and "ladder" are "escada" in Portuguese. :)
Then the translation/answer should be changed. Confusion is the biggest obstacle to learning anything.
How would you change it? There are some translations between English and Portuguese that will always be ambiguous without context. However, since a staircase cannot be moved much less carried by one person I don't find this sentence to be ambiguous.
Não da para entender muito bem o motivo pelo qual não aceita "stair'' por que tem que ser "stairs"?
Pelo que eu sei: stair=degrau, stairs=escada.