Everytime I hear these claims, it makes me want to gag.
You have to remember the "selective" wording in their claims. Granted, its been decades since I was an investigator but I seriously doubt policies have changed.
No department ( State,Federal or Military) I have ever heard of has the authority to hire on a psychic in any "official" capacity. ( they would have to be academy trained and hold cert before they could be considered "official")
It would be "possible" to bring one on as a consultant for a specific thing. ( it has been done in other fields) But for a department to make such a request, the case would have to be super critical and the "contracted psychic" would have to have a verifiable CV where they actually SOLVED something before such funding would be approved.
I cant say its never happened but I personally have never heard of an actual verifiable case where a department "officially" contracted the services of a psychic. I've never heard of a psychic whose claims were specific enough to be verified in order to be approved.
How they normally make these claims ( and stretching the truth and seriously playing on words) is that some of them become "private investigators" thru whatever state requirements apply. ( thus they can carry the title of investigator or detective- they just cant claim they are state sanctioned LE)
Now, in some cases, a PI "can" be brought in to assist in an investigation by an agency. ( the psychic kinda plays with words) They are being brought because they may have a relevant skill or simply because that department can use licensed PI's for some "consulting" or special duties. These instances are rare but have happened.
The most common way they "get involved' is to be hired by the family and most LE agencies will tolerate that but wont let them near sensitive case information.