The point here is more that a circle has the same diameter regardless of orientation. There's no way to rotate it to make it fit through a hole it couldn't before, like you can do with a rectangle.
The height of an equilateral triangle is about 87% of the length of one of its sides.
In particular from https://en.wikipedia.org/wiki/Prince_Rupert%27s_cube
> In geometry, Prince Rupert's cube (named after Prince Rupert of the Rhine) is the largest cube that can pass through a hole cut through a unit cube, i.e. through a cube whose sides have length 1, without splitting the cube into two pieces. Its side length is approximately 6% larger than that of the unit cube through which it passes. The problem of finding the largest square that lies entirely within a unit cube is closely related, and has the same solution.
That 6% larger is the key.
My theory: They're heavy, so making it a circle at least eliminates the need to "align" it when putting it back. You can basically just drag it using a hook and it'll slot itself into place.