I don't think that LE is trying to discourage people from searching as a general rule.
I believe that the statement is meant to keep people with motives that are not pure from searching. We heard a local tell us about a searcher last week that kicked the door in to a private office after the homeowner had given them permission to search his property. WHY? What gave anyone the right to kick a door in? There is something wrong when you cause damage and go into the property of others. This is what LE is trying to stop. Because if you cannot follow the basic rules of search and follow the law, what if these searchers did find Hailey? Or evidence? What would they do?
I believe there is some type of evidence that came very early on in the investigation. Phone pings, phone records between Shawn and Billie or something in this regards that led the investigation where it is going.
As far as the search dwindling? It appears there are many egos out there and if anything, that is affecting the searches. It could be the fear that people are violating the rules of searching, that people are doing this for the wrong reason and that people just are afraid to get involved.
Or people may feel that she is so well hidden, buried etc., that after 3 months they have to go back to their own lives and let professionals take over.
I think the reward was changed in order to get a tip as to where Hailey is so that professional searchers would have some clue as to where to start looking. That is allot of country out there and it is needle in a hay stack. 3 months into the investigation, the fires, weather changes, people tromping around out there, changes in the topography now with grasses and crops, it is a needle in the haystack.