No. Tell that to the family members who find lawyers who will still sue and win huge judgments.
You know the amount of people who lose their jobs and livelihoods when something like the scenario above happens?
The margin of error in the US for doctors is 0%. The doctor that did not recognize the signs and symptoms of that kid who died from runny nose most likely ended up with a M&M, has that mark on his record when it comes to getting other jobs, and his future employers who pay his malpractice have to pay higher premiums because of it. Making it damn near impossible for him to get a job.
On top of this imagine the RN who also was responsible for triaging this patient. Something like this (I can't even mention the situation but it had nothing to do with runny nose/CSF) happened to a co-worker of mine. Actually, it was almost to the letter of what happened in OPs situation except the patient went home and died after refusing treatment. Their family didn't even care about them or live on the same side of the country state as them. But because they were opportunistic they sued the hospital I work for and won a huge settlement. The doctor responsible for allowing them to leave was eventually forced out of their position and had to go into aesthetic medicine because no one would insure them as an ED doctor. The nurse who was responsible for that patient lost her job and almost her license because the hospital, attempting to limit all their liability, passed the buck off onto the individuals involved.
If OP was allowed to refuse treatment and go home even if he was able to answer questions properly then died and his family sued for malpractice or negligence they would still win.
On top of this this is going to be a fruitless effort for him. Do you know the number of patients who try to file the same suits and end up losing once the doc sits down and says "I have never met the patient before so his baseline mental status was unknown to me. He was in a serious motor vehicle accident that involved spinning out. It was unknown if he had a traumatic brain injury, or had alcohol and drugs on board. There was no way for me to know if he was in an altered state from drugs, alcohol, or a brain injury without acquiring testing he was refusing to allow us to perform. For his own safety I had him restrained, sedated, monitored, and drew his blood and performed a CT Scan."
There are thousands to millions of patients who receive this sort of treatment every day and every week in a hospital and they never win any judgments.
I really doubt that OP has a lawyer that is anything more than a shill willing to take this case. I've been an ED RN for 5 years and have heard thousands of people complain that they will sue for being treated the way OP was treated. Not once have I ever heard my supervisor discussing a case like this even going to court. And trust me, every time someone decides to file civil litigation against a hospital and you were the RN involved in that patient case the first thing that happens is the Risk Management department contacts you and makes you sit down to discuss what you remember and what you documented. I've personally had hundreds of people threaten me with lawsuits for restraining them when they were intoxicated (not saying that OP was) so we could make sure they didn't have serious brain injuries after being assaulted or getting into car accidents.