I don't think this is true. The "simple" model of refrigeration taught in highschool is just a carnot cycle running backwards, and this can be modeled with an ideal gas. The author of the post covers this the section on "the Thermodynamics 101 Answer"[1], where all you need to drop the temperature of a gas is to let it do work on the piston.
That's not to say that JT is not useful, just that we can explain a theoretical refrigerator without it.
[1] https://mattferraro.dev/posts/joule-thomson#the-thermodynami...