Fourth Amendment to the United States Constitution
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
Doesn't say anything about "except squatters". Who's the twit now?
You can't just stop junkies on the street and search them without probable cause.
Now these tents present a problem ~ but probably not in DC since it's not in the 9th Circus jurisdiction. In general the courts here have held you pretty much need a permit to do stuff on public property. There's a lot of demand for that public property and if you just let folks enter and do what they wanted pell mell you'd probably have fights.
There are no campgrounds on the Mall. At the same time the Boy Scouts got permits and camped out once a year. So there is a permitting process for tents in the federal district.
It says Houses, not Tents.