The explanation provided is correct only if a figure inscribed within another is a figure whose vertex touch the outer figure. That being the case, "the perimeter of a triangle inscribed in a circle can be infinitely small".
But according to Wikipedia, "an inscribed figure is one that is enclosed by and "fits snugly" inside another. There must be no object similar to the inscribed object but larger and also enclosed by the outer figure." http://en.wikipedia.org/wiki/Inscribed_figure
Therefore, the largest possible perimeter would be 3*sqrt(3) (for an equilateral triangle), while the smallest possible perimeter would be close to 4.
I believe GMAT employs Wikipedia's definition of an inscribed figure.
Please kudos if my post helps.