Here is my opinion on why they are denying the private organizations.

If a private organization has to take over they have to perform all the same procedures that TSA would. However, considering how close TSA walks the line of what is acceptable and unacceptable and IMO frequently jumps way over that line, then I believe many of these private security employees would be taken to court since they do not have the government protection that TSA has.

Once in court TSA could be forced to reveal things they consider SSI, or worse yet a judge could rule that the procedures that are taking place are a violation of a person's right to privacy and then everything else goes.