I think this is a fine line. Ex-difficult child did not WANT to go to egbs. Why should he have desired Tx? It was definitely all our fault--he believed that and his Goth crowd reinforced it...
However, he was 14 and I could force him to be there. They could (gently) make him uncomfortable if he didn't participate. After a while, he began to feel better (depression lifted) and he thought it was for the best to be there and try to get his life together. He also knew it was a set program that he would leave upon completion--not an open ended "sentence"--so he had a target to work toward. At the beginning, I was afraid he would be kicked out as too severe, but after about 6 months, I knew it would work well enough that he would complete the program.
So in my opinion, the child has to try, but parents sometimes have to force the opp'thank you for Tx.
The younger the child, the better compelling Tx works which is why I think ex-difficult child's outcome was better than some of his peer group at egbs who were 16 or 17 at entry.
Martie