I would handle the situation in this way:
Try to call the patient first to get them to explain the ASA allergy.
Then one of three things happen: 1) they have a BS allergy (like everyone has pointed out = tummy upset) so then it gets filled.
2) If they don't know or don't answer I'd call the MD and have them double check the patient's chart there for any allergy details and ask if they want you to dispense. If they say yes, document this and make a note on the bag to have the patient talk to the pharmacist at the time of pick up.
3) if they say they had a true salicylate allergy with wheezing, angioedema, bronchospasm, etc then I would not dispense, call the MD and explain, tell them you are NOT dispensing the med even if they say to, document this, and if the patient gets mad and wants to buy it OTC at their own risk then great.
I wouldn't fill ANY NSAID's for them in this case just to make sure your butt is covered. If a person has a true aspirin allergy they probably will be happy to not take a chance on taking any NSAIDs.