Most of the people who 'choose' street life have truly awful alternatives. Drugs, mental illness, family abandonment, etc are often at play. Convincing themselves that they want to be homeless can also be a form of adaptation to make the condition more bearable.
The article addresses that. If you thought big brother was watching you, this would seem to fit nicely into that, wouldn't it?
I've seen a few interesting discussions of this idea with regard to mental illness in general.
If someone says they think the government can track their location at all times, is scanning their phonecalls, and shares that data with an international conspiracy... are they schizophrenic, or just talking about the NSA sharing data with Five Eyes?
If you ask somebody to sign a narrow, research-only privacy waiver for a drug trial and they say you're going to share that info with a tech company that already has a secret profile of their entire life... the NHS did pass private medical records to DeepMind.
If they say online ads are talking to them personally as part of a coordinated campaign to brainwash them, it turns out you can have that done to somebody for $30.
It doesn't particularly seem like this is a general problem in terms of diagnosing or treating people; paranoia disorders follow pretty clear patterns of thinking, and they're usually self-validating whether or not there are actual conspiracies afoot. But the specific case of asking people to sign consents and agree to monitoring seems like a major hurdle, and I've seen some doctors point out that they can't even choose low-intimidation wordings because consent forms are usually written by legal to cover all possible cases.
The basic problem is that no matter what you find in terms of unregulated off-the-grid living, you need to own property in order to legally put up a permanent residence. Generally this involves being a titled landowner, which requires paperwork and in basically all cases payment, either to purchase land or via property taxes. (You can find local governments offering free land, but it comes with extensive rules and at most temporary property-tax exemptions. Tax-free land, meanwhile, will have to be purchased since homesteading is no longer legal. The newest direct homestead claims were made in 1986, while the indirect tactic of patented mining claims ended in 1994.) You could potentially get a landowner to guarantee you such rights for free, but that still sets a minimum standard of legally-binding paperwork signed with the owner.
Option one to avoid paperwork is to live off the grid without a fixed address. Lots of 'tiny house' residents build homes that are in principle movable to avoid building code hurdles, but they generally own property; I'm not sure where it would be legal to park a mobile home or towable cabin indefinitely, but there might be places. You could live out of an RV or any other property that genuinely does relocate, but that's going to mean filing paperwork to keep a vehicle registered. Finally, you could abandon even a semi-fixed residence and just permanently camp on public lands. As far as I know this is legal if you can survive doing it, but you'll generally need to follow some inconvenient rules; through much of the Southwest you can camp freely on public land if you relocate by at least 25 miles every 14 days.
Option two is to live illegally with an eye towards eventual legal ownership. Adverse possession must be "open and notorious" and generally can't be used to obtain government land, so you'd probably want to check out state laws and choose an abandoned mining claim or other unattended property. (Montana has remote land and particularly favorable rules for this sort of thing, and Alaska of course maximizes open space.) This will involve quite a lot of paperwork and lawyer's fees if the original owner contests your claim, but that's true of any legal challenge. Since title can be created without proactively filing any documents to show ownership, I think this counts as "without paperwork".
To my knowledge, the 'traditional' approach where you build a fixed cabin somewhere and it's legal from day one without paperwork is completely impossible. Doing it with paperwork but no payment might be possible, but I don't know of a way.
Where can I get one of those free cabins, and will my friends join me?
They're still American citizens. By what mechanism do we determine that they're psychotic and therefore not allowed to live off the grid? Do we lock them up in a psych ward until they "admit" to their insanity, for the crime of ranting?