Any member of the public can request a death certificate, so there isn't really any way of keeping it secret. Simon Fuller might be a shit, but he doesn't have that kind of power. The coroner also doesn't cover stuff up, they just observe what it is and write the certificate. The vagueness does suck a bit, but I've seen it used where the coroner is just like "There obviously wasn't foul play, so I won't go massively into detail." I agree it would be better if he said which organ failed, but sometimes they don't, it doesn't indicate a cover up.
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Was it definitely professional paps and not someone out and about with a phone camera?