I hope this message finds you well, present circumstances excluded. I am a licensed attorney with over a dozen years of experience handling matters of this nature. It is a pleasure to assist you today, though I am sorry you are going through this issue.
Your thoughts are keen and may be true. However, if your son is on your insurance, it is in his best interest to have that information available to this provider. There are a couple of reasons why this is the case. Under Colorado law, as well as most other states, they do have the ability to keep him if he presents a danger to himself or others as determined by a physician. This could drag out. Since he is of adult age, the expense associated with the care will be billed to him. As such, through no fault of his own, he could leave the hospital or treatment facility owing a lot of money. The insurance can and should prevent that being the case.
The other issue here is that your insurance company processes claims like this all of the time. The insurance company will tell the provider they are not going to continue to pay if the treatment falls outside of the norms established in the insurance industry. Once they realize they are not going to be paid, they will seek to discharge in most cases. So, the insurance company can actually be a good buffer for you guys under the circumstances.
So, there is financial liability to him if he does not have the insurance on file. Moreover, the insurance may help expedite him getting out as well. I recommend that you provide this insurance information.
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Thank you and best wishes!