Overweight people are still more likely to have heart attacks. This study did not address that, just survival after a heart attack. From everything I have seen, losing weight is a good idea to prevent future heart attacks.

It could be that heart attacks in overweight people have different causes than in non-overweight people and therefore the survival rates may be different. For example, non-overweight people may have a lot more blockage of their arteries than overweight people before they have a heart attack. This could mean that the consequences of a heart attack are more serious for non-overweight people, because something in their thinness protects them from having a heart attack until the situation in their arteries is really serious. I have no data to support that hypothesis -- it is just a hypothesis -- but as someone noted I am a researcher and I can tell you that knowing something is related to something else doesn't mean that one causes the other (in somewhat technical language, correlation is not the same thing as causation).

It's like saying that people who are overweight are more likely to be diabetic. That's true, but it doesn't mean that being overweight causes diabetes. It could be that hyperinsulinemia causes both diabetes and weight gain.

Also, while BMI isn't an accurate gauge of fatness/obesity in any one person, I think it is pretty good across the population, and this study presented results for groups, not for individuals. I think we can be assured that the group with a high BMI was, on average, fatter than the group with a low BMI, although there may be individual exceptions in each group.