I think the critique has been beat enough.

There is a type of stroke which could be made much worse by aspirin, a hemorrhagic stroke. Otherwise known as bleeding into the brain.

But, as so well pointed out, for people with even a smattering of diagnostic skill a stroke and heart attack are not all that easy to mistake for one another.

That said Leigh_Ratcliffe makes a good point about not assuming too much or jumping in too soon. Keeping the person calm and calling 911 is not bad advice. Most city and suburb dwellers are so close to 911 advice and EMT/rescue services that waiting until your advised to give aspirin or for the troops to arrive isn't much of a risk.

There is certainly still some risk of an unknown allergy or unexpected interaction. Some number of people likely to have a heart attack are already on aspirin and/or other blood thinners that could make them very prone to bleeding. So stuffing aspirin into people you happen to think are having a heart attack isn't something you want to do casually. Every therapy and drug has side effects. Don't go off half-cocked.

In more remote locations, or when emergency services are overwhelmed or unavailable, your much more on your own. Assuming 911 still works and realizing that EMTs are not on the way they may advise you to administer aspirin.

I don't carry aspirin on me but all of my first-aid kits have some aspirin in them. Even the tiniest one has a couple of single-dose foil packets in them.

Aspirin is good stuff. Good for fevers (But not for kids because of Rye syndrome), headaches and moderate pain. Also not for a person with serious bleeding, internally (As is possible after an auto accident or hemorrhagic stroke) or the much more obvious external bleeding.

Generally Tylenol is safer and less likely to interact with other drugs but it is much more toxic to the liver than other OTC pair relievers. So don't take Tylenol for a hangover or when the person is jaundiced or shows signs of their liver being under stress. But Tylenol is good. It will take the edge off of a lot of pain.

Generally Ibuprofen is my go-to pain relief for joint or bone pain. It seems to work better for this than Tylenol.