They're refusing treatment because they're addicted. They're refusing shelter because the shelters have policies (like not using drugs, or from the article; no pets) that they can't meet.
A lot of them have been abused by the institutions that were supposed to help them in the past, so understandably don't trust that they will be helped by similar institutions now.
Any of us, put in the same situation, would find it impossibly hard to deal with. I was lucky; I had friends who could help and I got lucky with some work that allowed me to get out of that situation. If I'd not had that luck, I could easily have gone down the same road.