1. If I am going to kidnap a child, the LAST thing I want in my possession is a de facto tracking device. Cell phones, even if turned off, can give off pings and let LE know where they have been. Some even have gps.
2. If I have harmed my own child and had a cell phone with me when I was hiding the body, I would definitely want to be rid of the cell phone. I might even claim they were stolen by whoever took my child.
I really hope these parents are innocent and they get their precious little baby back. But this just looks hinky to me. Sorry.