Firstly,
just so you khow, the current standard in most states is on the say-so of a doctor and a concurring opinion by a second doctor. I’m not sure what you think the standard is, so apologies if I’m telling you something you’re well aware of.
Secondly,
It’s not like a psychiatric professional is ever in a position to know that “nothing is wrong with them”. I mean, it’s not like they can test your blood for the presence of serum schizophrenerase and it comes back negative and they send you home.
Both now and in the past, it can help if plural numbers of solid well-placed citizens show up at the facility to visit and the patient persistently but politely indicates a wish to leave.
I myself am not sure how the laws worked back in, say, 1910 or 1927, but for a long time (including the era before the shift away from permanent institutionalization) you were entitled to a legal procedure, a commitment hearing, even if the doctor felt you needed to stay incarcerated. The rule I am familiar with is the “72 hour” (aka 3-day) notice rule, where if you indicate that you wish to be discharged the institution has that long to consider committing you involuntarily. It was and is often a bit of a rubber-stamp process, where the judge assumes the doctor knows best and views it as a medical, not a legal, question, but you’re entitled to legal representation and a good attorney will try to get a dissenting psychiatrist to interview you beforehand.
With that in mind, if the psychiatrist is aware that you have the wherewithal to obtain good legal representation, they can shrug and decide not to pursue the matter in the court, rubber stamp or no.
There are many people in the modern and semi-modern era who have attempted to check themselves in, stating that they’re depressed and suicidal, only to be sent home and referred to outpatient treatment. The cynic in me reads it as “if you’re sane enough to know you’re sick and need help, you don’t need to be locked up, but if you think you’re not sick, you’re sick”.
What they’ve always looked at is whether or not you are upsetting other people and hence disrupting the community and whether you can function in the community. If a neighbor, relative, employer, or police officer made a complaint that resulted in you being brought in for observation, you’ve already “upset” someone and they don’t want to err on the side of underestimating how disruptive you might be, but yes they themselves aren’t as much of a rubber stamp as the courtrooms tend to be. They tend to be the type of conservative that views economic and social stability as concurrent with mental stability. (That’s why having supportive friends come visit helps).