Unless you are an M.D. you SHOULD NOT give asprin to a suspected heart attack victim.
I can't say I agree with this advice in every case (trained vs. untrained responders, family vs. unknown victim, etc.), however one interesting thing:
Back when I was a paramedic running ambulance duty, we could give morphine on standing orders but required a direct order to give aspirin.
"Standing orders" mean you are following a defined protocol, but you as the paramedic make the decision to procede or not yourself in the field. "Direct orders" mean you have to radio in to the hospital and get a physicians consent before proceding. The protocols you follow as a paramedic are goverened by your "physician advisor". They decide what you can and cannot do, and what (if any) advance authorization you require before proceding. A different ambulance service than mine could well have given aspirin under standing orders, but had to radio in for a direct order for the morphine. This was many years ago. Maybe protocols are more standardized these days.