CLICK HERE to see a Grammarphobia article. I wonder if this language usage is just within the medical profession, because I had a nurse practitioner ask the same thing: "You are allergic to no medications?" I answered, "I'm not allergic to any medications I've taken."
In telling this to my brother he lectured, "But you knew WHAT she meant; there was no need to insert your clever correction." (OOOOOH! "Clever correction." He knows I love alliteration!) I said, "But it sounded stilted." "Stitled?", he gibed!
I answered, "It's like, yes, I have no bananas! If I'd answered 'yes', it would have been yes, I am allergic to no medications; if I'd answered 'no', it would have meant no, I'm allergic to medications." He answered, "That's rather convoluted, doncha think?" I said, "She should've asked, 'Are you allergic to any medications you've taken?' doncha think?"
From the OED: stilted: adjective "of a manner of talking or writing: stiff and self-conscious or unnatural." synonym: awkward
Listen to 1923 recording of Yes, We Have No Bananas.