This is such a dumb argument to have, and I'm confident everyone knows this.
If the definition of a square is a rectangle with all four sides equal, it doesn't matter if a shape is officially recognized by the "Quadrilateral Society" and receives an official designation verifying that it is a square
... if it is a rectangle with four sides of equal length, it is the very definition of a square. The designation just assures everyone else that the square has been verified, like an official certificate of validity.
If someone can't tell that a shell is a shell, can you trust anything else that they say?