If LE knew that Erica was not missing, and then allowed The Dr Phil Show to say that she is, it would be akin to yelling, "Fire!" in a crowded movie theater. And if the show was breaking the law I'm sure LE could get a court order to stop it from airing. Dr Phil isn't above the law and he isn't an idiot, either. You can bet that his extensive staff looked into every detail, including checking with LE. It's just common sense.
You have a good general point, but your specific analogy to yelling "Fire" in a crowded movie theater is perhaps not the best (that's not a cut-and-dried no-no, but involves motive and other factors).
The show probably wouldn't be breaking any law by claiming Erica's missing if they know she's not (depending on the reason for the disparity between reality and spin), but saying that Dr. Phil's staff looked into the matter thoroughly is more relevant and you're making a very good point there. The Dr. Phil Show would lose its audience immediately if there were ultimately no justification for such a "charade."
But it is so common for cases to involve back-tracking on the facts that most people take it in stride if it's "explained away" later to their satisfaction. The pliable public has a way of turning on a dime, 180 degrees, depending on which way their nose ring is being jerked.
Regarding the hiding-Erica-from-James theory, the biggest hole (as has been pointed out) is that Casey and Sandy could tell LE and request that it be kept confidential so that James couldn't find out. On the other hand, James has already assaulted his mother with a baseball bat, and if he found out that Erica was being hidden from him, he could become homicidal towards one or both parents, and maybe even other family members ... a good reason for CP & SP not to reveal specifically where Erica is.
As for the idea that Casey simply gave Erica away, it just doesn't fit Casey's money-hungry profile.
But selling (there's a nice lump sum) or killing Erica gets rid of the caretaking effort and leaves the regular government checks intact ... as long as she's not reported missing. If there was a murder, I'd say it was probably accidental (perhaps by Sandy), just because Casey wouldn't simply kill a child on purpose that she could instead sell and get money for in addition to the future ongoing government checks. She's too conniving to simply kill or give away a potential source of income (unless the killing were accidental).
How about this (the idea of selling Erica hasn't yet been deeply explored so far as I know): Say Erica was sold to a child-trafficking ring (or even a sex-trafficking ring) that is run by organized crime. Speculate that Casey received a very nice sum of money in the Mooresville McDonald's parking lot, while Sandy was waiting out of visual range (he couldn't see Irene "Nan" Goodman OR the possible money transaction ... so did Casey have to walk over there, or did Sandy drop her off and drive some distance away?). No documents were signed, and no paper trail was created. Let's say it was understood that Casey and Sandy would be dead ducks if the ring were ever about to be revealed, so Casey dreamed up the perfect explanations for everything (Erica was entrusted to Irene "Nan" Goodman, the [oops! already dead for 3 years] mother of Erica's biological father, Willliam "Billy" Goodman, after which all avenues of contact with Nan and Erica magically disappeared). The denial by Erica's sister Brooke that she went to the Asheville area with Erica and her parent(s) could fit in with the sale theory, where the true buyer's(s') identity(ies) have been withheld (and were possibly never known) by Casey in favor of her story about entrusting Erica to the care of her [oops! already dead!] paternal grandmother. Casey could have fabricated the story about going to Asheville ... or maybe she just has a really fragmented brain and memory.
Consider the three most viable theories: murder, sale, or give-away. For Law Enforcement, digging up the Parsons' yard, looking for a dead body, is part of the process of elimination. A dead body proves death (from whatever cause) and provides possible evidence that Erica was not sold or given away before her death. Not finding a dead body there or elsewhere leaves her possible death unresolved, and also keeps the other two possibilities open (sale, give-away). If organized crime were involved in a sale, then Sandy Parsons might be particularly frightened because even if he could escape conviction and jail or the death penalty for murder, he would be killed by the crime ring (likely disguised as a "suicide" or "car accident") long before the ring's existence could be discovered.
I thought Sandy looked a little scared on the Dr. Phil Show, but I chalked it up to his being unaccustomed to that environment, as well as being a less verbal man. But other people on this forum say they saw a great deal more fear than that in his eyes. What if he knew he was going to die soon, no matter what, just because of the media spotlight on finding Erica? That would strike fear into his heart.
At this moment, I'd lean towards the organized-crime-ring sale first, and the accidental murder second, except for James' claim that Erica was killed by one or both parents (is he even credible?).
This is pure speculation, of course, and totally unfounded.