Is It Finally Time to Accept Fat as the Sixth Taste?

There are five acknowledged tastes: sweet, sour, bitter, salty, and (slightly more controversially) umami. For awhile now, researchers have suggested the existence of a sixth taste: fat. Now, a new study has researchers saying they may have finally isolated it—and they’ve given it a name: oleogustus.

Source: Is It Finally Time to Accept Fat as the Sixth Taste?

Fat seems like a broad term to me. Pig fat (lard) has a vastly different taste than butter (milk fat), and both are different than olive oil (plant fat). All have very distinct tastes. Does oleogustus encompass all of those? Do all fats have that exact thing in them?