There has to be more than just 'missing home' to be hospitalized against one's will. Did you know if the roommate mentioned anything about harm, suicide, violence, or plans? I know those are often the things that could trigger such a response (from most mental health professionals and mandated reporters).
If that is true (getting locked up for strictly only mentioning missing home), then it's really dangerous when people go seek help as it can work against them and they have (little or) no recourse against the counselor. It's even more fucked up that said person would then be held legally responsible for the medical/hospital bill as a result of being involuntarily hospitalized. This makes my blood boil with furious rage, not only did the shithead counselor over-react (assuming that there isn't more to the story), the poor patient is also on the hook for medical bills stemming from such an unfortunate ordeal. Then all of this is somehow legal and there is no recourse/redress from this debacle makes me angry at the whole system. That case certainly isn't the first and certainly won't be the last. At any rate, I hope your child's roommate is able to fight against the hospitalization and also defer the bill (which is bullshit as it's involuntarily forced on him/her).