The main underlying reason for the conspiracy theories is the complete lack of trust in the MSM, in my opinion. We saw how they helped the Obama agenda with Benghazi. So when the MSM gets parts of the story wrong with Sandy Hook, it will happen that people will think something is amiss. And especially when so many members of the MSM turn around and use Sandy Hook to blatantly shill for gun grabbing.
Pretend for a moment that you are an immoral devious narcisstic politician who is capable of Fast and Furious and god knows what else. You have stated in your early years that you want to confiscate guns.
If you are capable of Fast and Furious you are capable of setting about a situation like Sandy Hook.
But, how to distract from it?
Gin up the conspiracy that Sandy Hook never happened . Make sure enough conflicting info gets out there to set people off on the conspiracy bandwagon. Is this just a random nut that went on a murder spree? It's possible...or maybe he had a little help.