[KMnO4]

That is correct. Vegetable isn’t really a botanical word since you typically refer to the specific parts of the plant (eg root, bulb, leaves, flower, fruit, etc). Vegetable is just a catch-all to cover “parts of the plant we eat”.

Fruits have a specific definition: the seed-bearing body of a plant produced by the ovary after flowering. I.e. if you have a flowering plant, the “fruit” is the part that contains the seeds.

[gumby]

... And the watermelon, like all gourds, is one of them: a plant cultivated only for its fruit. That appears to be a bug in the blog post. Some plants, are eaten both ways (both the fruiting body and leaves or other body parts are consumed).

With fungi we eat only the fruiting body, but nobody calls them “fruit” except in the superclass sense (“fruit of the land”)

[catlikesshrimp]

We don't call them fruit, we call them mushroom. And they can't have fruits, as in pear tress or other angiosperm plants, because mushrooms aren't plants.

The fruiting body, which is not fruit, doesn't have seeds. They have spores, I think.