It is entirely possible that the hospital knows what happened and why the person died, and are just not sharing it (maybe to respect the family's privacy, for example).

Having said that, I do think you're right, the cause of death should absolutely be shared, otherwise it looks quite dodgy. If he was indeed discharged with "one of the cleanest bills of health I’ve had in a long time", then how could he die so shortly after, and why would there not be more discussion around the specifics?