Unfortunately, I have personal experience with the civil commitment process; I see two issues.
One is the basis for the civil commitment. I have a difficult time believing that the police would send a private ambulance service to a private residence, without also sending a police officer knowledgable about civil commitment laws in an emergent situation. That means that Officer Friendly, who arrived on your doorstep, had a conversation with your daughter which led the officer to make a conservative call to have her evaluated.
There will be a record of this interaction. The police department will have a form to request the incident report. You'll want to order that.
I'm hard-pressed to believe that a person who answers the door, sounds rational and does rational things (like, ask Officer Friendly if the officer can call her mom, because she was just doing her homework listening to Beiber when the Loon Platoon showed up) would have ended up being transported for evaluation. Police officers are used to dealing with accidental calls and pranks as well as actual emergent situations - they arrive, evaluate and respond accordingly.
If you haven't already done so, you may want to schedule a meeting with the former friend and her parents, so all of you can sit in a room and get some clarity on what happened. Preferably, do this with the incident report in hand, ready to pull up text messages, social media posts and anything else that provides context to the situation. If the former friend had a credible concern, and the incident report shows that your daughter is perhaps not being forthcoming on what she said and did, you need to know this so you can deal with your daughter. If this was a malicious prank, that should become clear during the meeting, and the former friend's parents need to know what their kid did.
(If you'd rather go the legal route than the parent-to-parent route, get the incident report and review it, then consult with an attorney.)
The second issue is the bill. Like the poster above, I'm wondering if this was submitted and denied by your insurance; not submitted at all; or you don't have insurance for your dependent child, in violation of the mandatory insurance requirements of the Affordable Care Act. If it's a denial, work with the billing department of the ambulance service - maybe it was submitted with an erroneous code and can be re-billed properly.