Unsane - Being held against will

In the movie Unsane (2018), the protagonist, Sawyer Valentini, goes a private psychiatric clinic because she suffers from stress after having been stalked. She briefly speaks with a doctor who asks her if she has suicidal thoughts. She answered "I have, in the past." Then, the doctor asks Sawyer to sign some papers and... voilà, she is held against her will in the clinic for seven days and the thriller begins...

My question is: Is such a scenario legal/plausible?

Other useful information:

• No relatives, friends, or coworkers of Sawyer are contacted by the private clinic.

• Sawyer made a call to the police saying that she is detained in the clinic against her will. Later, two cops came to the clinic, checked the papers (without meeting Saywer), found everything fine, and went way.

• Saywer's mother, after knowning that her daughter is held prisoner, went to the police which told her: "I understand, Mrs. Valentini. But there's nothing we can do unless you have proof that a crime's been committed."

• Saywer's mother also talked to a lawyer, who replied: "Pennsylvania state law mandates that a patient can only be held on involuntary commitment for seven days without a court order. And, look, they're not going to go to the hassle of getting a court order after her insurance stops paying. Is it inconvenient? Sure. Should something be done to stop it happening? Absolutely. As your lawyer, is it my priority getting Sawyer back into your care? It's number one. Keep me in the loop about the situation. If you think there's legal cause to intercede, I'll get right on it. (HANG UP)"