An anarco-capitalist (an anti-rand) libertarian flavor) rejects involuntary commitment as a matter of dogma. So these institutions cannot exist, even if they are following the "law".
Furthermore it is the state who has monopoly over violence that legitimizes this behavior (the history of physiology, involuntary commitment, and state violence is rich and fascinating).
Libertarians see this as violence over an individual. Not being the initiator of the violence, the victims have a full moral right to use violent means to defend themselves, up to and including deadly force.
Right or wrong, these "free market extremists" have a more nuanced position than "the market will sort it out"
However, it seems clear that pressure to profit, pressure to grow fast, to raise ever larger rounds, etc. leads to huge missteps, both in tiny startups and in huge corporations. If you replace "beds" in that quote with "bank accounts" you get the Welles Fargo scandal. Ditto for Theranos. And these are only the very recent examples (that we know of).
Don't worry, free-market ideologues will coolly tell you. Their logic will seem airtight: over time, if Intake's psychiatric wards were really, truly locking up sane people who don't want to be locked up, the reputation of these facilities would no doubt have already suffered by now, and the company would have already been forced to close them. These incidents can only be isolated cases, regardless of the evidence. The profit motive will keep the company in check.
If you believe that, you haven't read the article.