Correct. Promoting aspirin as "good for the heart" is too generic of a phrase; such generalization may lead to healthy people unnecessarily taking a daily aspirin just because it is "good for the heart".

Aspirin is prescribed for some specific conditions due to its antiplatelet effect. From what I understand, for normal healthy people, there isn't much benefit of daily aspirin. And, there is potential for some side effects -- in addition to the same stomach problems / heartburn issues that plague other NSAIDS also has some bleeding type issues due to the antiplatelet effect.