I don't really believe LE bold faced lies to the parents of abducted children, especially by telling them that they suspect someone in the family if that's not the case.
In other high profile missing persons cases LE has been known to be silent, to not share evidence and to not keep the victim's family apprised of all of the developments, but that stems from a desire to keep the criminal in the dark about progress, convict the guilty party down the line and to keep certain key facts unknown to all but LE and the criminal.
I take the things K and D tell us with a grain of salt, but only because their interpretation of events has been filtered through panic, fear, hope and desire for Kyron's safety. I don't believe that Kaine and Desiree would completely make up the story that Terri failed her LDT, and that she told all and sundry that she failed including LEOs stationed in the Horman home at the time. I don't believe that was a lie. I don't believe that Desiree lied when she said that Terri complained about being leaned on by LE because of her cell phone pinging unrighteously.
But I do withhold judgment about Desiree's characterization of Terri's demeanor on the phone, for instance, or Kyron's increased crying before returning to Kaine and Terri's home -- because Desiree is clearly heartbroken, frantic, terrified and looking for answers. Just as we dissect every word and facial expression here for clues, D must be doing that times 100. And it will come across in her words. So while I think the shades of meaning might be emotionally skewed, and understandably so, I don't believe Kaine, Desiree or LE are outright lying to us in the press releases.