Who is doing the ignoring? what is the age of the person? why are they requesting aspirin? how do you know they are having a heart attack? It's not always a simple black and white answer, because there can be many variables involved.
911 Dispatchers (as well as the pharmaceutical companies, but they have a vested interest in it) are telling people to take aspirin if they have a heart attack. There are also other reasons to take aspirin. If the patient wants to take ANY med (not just aspirin), should we let him? or rather, should a doctor let a patient's wishes guide his treatment path, or should he use his own clinical education and experience to treat the patient appropriately?
As a general rule, if you call for medical assistance, and a trained person shows up to help you, I would hope that you would let them determine treatments. I wouldn't say the patient's request would be ignored, but there could be some very good reasons why a person should not be given aspirin.