I don’t know if the laws regarding voluntary psychiatric inpatient treatment are the same across the entire USA, but in Indiana, no, he couldn’t have just left. Even with a voluntary admission, getting released before a doctor wants to release you is at minimum a 24-hour process. You have to sign forms about leaving the hospital against medical advice (AMA), which the treatment team then has 24 hours to approve or deny. If they approve, you’ll be released soon after, though if for example you submitted the AMA request in the evening, the care team wouldn’t have to approve it until the following evening, and you may still be stuck there until the next morning. But if they deny it (essentially saying you’re too big of a danger to yourself/others for them to comfortably let you leave), you’re stuck. They can take you to court and everything over it. It’s not as simple as saying “hey, I’m not really feeling this anymore, I’m going home”.
I’m a bit confused as to how Graham was able to leave the way he did. It sounds like he just walked through the front doors and nobody saw him or tried to stop him or anything. At all hospitals and facilities I’ve been to, number one, there are many, many locked doors between you and any door that leads to the outside, and number two, there’s staff/security of some sort in the front office/lobby area, in case someone manages to get through all those locked doors. Maybe this is just in Indiana, but it feels like a bit of a failing on the part of the hospital, IMO. The whole point of being there is that you’re suffering from severe mental health issues that can’t be dealt with at home - you’re being kept safe, you can’t just leave when you want to.