There's definitely a link. Perhaps not the death itself but their way of living an dying. We've been seing this for some years.
Michael wasn't able to handle his wealth and his health.
I've always thought that the way Michael treated his body was peculiar. Not only the continuous reshapings of his face but also the peculiar approach to health in general - sleeping in an oygen tent, etc.
Both, Michael and Elvis wanted to perfect their lives. To Elvis who came from a really poor family it meant: "Eat as much as you can."
Obviously both considered a doctor trustworthy only if he did what they demanded.
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