This is a very thoroughly studied phenomenon. The hearts of obese people are generally more muscular as you say, but not in a good way, so I wouldn't compare this to training. In overweight people, the heart walls get thicker and the volume of blood that the heart pushes out with each stroke is decreased as a result. This means their heart needs to beat faster to reach the right throughput and their heart is under constant strain, kind of like having your car overrevved at all times.

With exercise, the heart muscles grow in a different way, and the volume of blood contained inside is not reduced. So without looking at the heart itself, we can't even tell whether a lot of muscle is good or bad, we also need to look at the rest of the context.

I think doctors can figure out real quick which version of heart enlargement you have.

The athletes heart is going to beat at 1/2-1/3 the rate at rest compared to the obesity-enlarged heart and a stress test is going to show the athletes upper heart rate limits are much much higher.