I feel like the ransom demand was authentic, and based on the brazen, elaborate, and meticulous nature of the invasion, sent by this particular perp or perpetrators. Whether it was a legitimate desire for money, a diversion, or something else, remains to be seen. I feel like they want something from SG, but only those close to the investigation would know what that definitively is.
Why remove the 84 year old mother of a well known celebrity with means and then send the celebrity a ransom demand via a large media outlet if the plan was just to murder her mother incognito, and with no infamy or fanfare?
TLDR: She may indeed still be alive, and the reason for that would be anyone's guess at this point.
JMO.