Doesn't it make sense that, if you were taking a drug that reduces morbidity, you'll get increased morbidity if you stop it?

Not if having a heart attack within 1 year at a higher rate is an co-morbidity factor when the primary treatment was for obesity or diabetes (not stating that obesity and heart disease are not positively correlated).

To use a dense analogy: if I stopped brushing my teeth I would not expect to die of gum disease.