Problem is the lack of struggle to stay alive. Each one of them should have showed signs of a will to stay alive. Even the dog would want to live. They are lying to people.
Why does it take a month to find out what killed these people? I could see taking your good old time on a random pile of bones thats been out there for years but If I was in that area I would want to know what killed three seeming healthy people and a dog all at one time in short order.
Truth is fast.
Figuring a lie that might work will take a bit of time.