I've been sitting on my hands for a week now, I've read, and reread all I can on this case. I'm a former dispatcher and now work as a civilian in a law enforcement agency.
From my dispatching (and I am anxious to hear the 911 call) days...if he indeed reported that his baby was choking, then the LEO and EMS are dispatched to a child in severe distress from choking, a code 1 or priority 1 call (lights and sirens, clear the way a life is in danger). Upon arrival they find a dead baby in which rigor has set in, right then and there the story starts to unravel. The car smell "to high heaven", and again more unraveling. Of course, just based on that he's going to be questioned immediately, and an investigation will ensue. His story is not matching evidence, clear evidence at the scene.
It has also been my experience that LEO really don't like talking to the press, they really do not want any case to get media attention. LEO want to investigate, solve their cases and go home to their families.