DBHDS has said they don't want sponsored residential providers from moving to other organizations if they are closed by one organization for regulatory noncompliance... why should this be any different?

They have the ability to track this information already in place.  This additional work (and potential liability) should not needlessly be put on private providers when DBHDS has the capability and authority to manage this task themselves.  

Unlike DBHDS, most private providers don't have the luxury of hiring scores of people to handle administrative burdens.

Don't pass the buck, just take care of this yourselves.