What does it mean "to turn square corners?"

Solution 1:

The blog of Bruce D. Greenberg explains the legal concept:

The “Square Corners” Doctrine

Estate of Taylor v. Director, Div. of Taxation, 422 N.J. Super. 336 (App. Div. 2011). In FMC Stores v. Borough of Morris Plains, 100 N.J. 418 (1985), the Supreme Court announced the “square corners” doctrine.

That doctrine says, in essence, that in dealing with the public, government agencies must “turn square corners,” “comport itself with compunction and integrity,” and not “conduct itself so as to achieve or preserve any kind of bargaining or litigational advantage” over a member of the public. As the Court observed, this means that “government may have to forego the freedom of action that private citizens may employ in dealing with one another.”

Solution 2:

It is a direct reference to a Supreme Court precedent written by Justice Oliver Wendell Holmes that acknowledged that people must engage with the government on the government's terms. Holmes is famous for writing that is easy to understand by laypeople -- the idiom "to shout fire in a crowded theater" is also originated by him. Gorsuch is binding the federal bureaucracy to the same standard of formalism to which all other Americans have previously been bound.

Men must turn square corners when they deal with the Government. If it attaches even purely formal conditions to its consent to be sued those conditions must be complied with.

From Rock Island C.R.R. v. United States, 254 U.S. 141, 143 (22 November 1920)