I'm with you about the ransom appearing days later. I don't think we know if an initial ransom was sent immediately to the family, or not. DEVIL'S ADVOCATE: Maybe the kidnappers didn't like the fact that LE hadn't announced an original ransom, so they figured they'd go through TMZ, knowing they'd probably release it to the public.
I'm still entirely baffled why people believe it could all be a hoax. NG was obviously taken from her home - call it what you want, a kidnapping or abduction. If LE thought they were dealing with a homicide, they definitely wouldn't have NG's kids pleading for her return on national television all these days later. Regardless whether NG is alive or not (I hope the latter isn't the case), it would be difficult for kidnappers to care for an immobile, 84-year old woman with a pacemaker, in need of daily medication. You know what else would be difficult? Removing a body from her home, then trying to find a place to hide it.
FWIW, I am totally stumped.