This particular bit is about 90% truth, 10% lies. The biggest falsehood is the part that says, "Do not lie down."
It is true that you would do well to take an aspirin if you think you're having a heart attack, preferably chewing it. But the Bayer Quick Release aspirins are NOT appropriate.
Snopes says this is a mixture of true and false information: You'll find what they have to say about it HERE. Notice at the bottom of the page of information there are links to take you to the FDA website, where you can find the proper information.
New Aspirin---serious stuff