I'd say heart disease is more likely precipitated by other risk factors than NSAIDs. From personal experience I know my cardiac arrest came from obesity, poor diet, lack of exercise and other things. In fact, when I had my arrest, I wasn't taking any kind of pain reliever.
I do know again from personal experience that kidney disease sufferers are forbidden to take NSAIDs. It's a bummer for me because, as I get older, my joints hurt. NSAIDs would be better for the arthritis because they relieve inflammation as well as pain. I can take Tylenol, but while it might make arthritis hurt a little less, it does nothing for the inflammation behind the pain.
Those of you who can take NSAIDs -- I wouldn't stop unless your doctor tells you otherwise. Don't stop because of some mass hysteria promoted by Natural News.