This is done so as not to mess the institutions statistics up. If he makes it across state lines he is counted as "cured" If he messes up across state lines he is somebody else's problem.
Problem mental patients cam mess up an institutions stats very badly in this era where everything must look good on paper. Some of the direct care workers may have a "Thank God and Greyhound He's Gone" party if he successfully gets across state lines. Unofficially of course.
The social worker decided it was time for some Greyhound Therapy for Tim. Once Tim was gone she got a couple of the aides fired for allowing Tim to say such a thing to her.