Uh…

Watermelons are often viewed as a fruit, but they technically are a vegetable, related to cucumbers, pumpkins and squash.

…no. Merriam-Webster on fruit:

1 a : a product of plant growth useful to man or animals (as grain, vegetables, cotton, flax) -- usually used in plural <the fruits of the field> b (1) : the reproductive body of a seed plant consisting of one or more seeds and usually various protective and supporting structures -- used especially of edible bodies <squash vines full of green fruits that will be killed by frost> (2) : such a fruit having an edible more or less sweet pulp associated with the seed and usually being used as or in a dessert or sweet course <apples, peaches, plums, and berries are among our best native fruits> -- contrasted with vegetable <pears and cherries are fruits while squashes and beans are vegetables>

Merriam-Webster on vegetable:

1 a : PLANT 1c -- not used technically b : a usually herbaceous plant (as the cabbage, potato, bean, or turnip) that is cultivated for an edible part which is used as a table vegetable
2 : an edible part of a plant (as seeds, leaves, or roots) that is used for human food and usually eaten cooked or raw during the principal part of a meal rather than as a dessert -- contrasted with fruit <the tomato though botanically a fruit is usually eaten as a vegetable>

Merriam-Webster on watermelon (emphasis added):

1 a : a large oblong or roundish fruit having a hard green or white rind that is often striped or variegated and a pink, yellowish, or red pulp that contains a copious sweet watery juice and many seeds b : a vine (Citrullus vulgaris) that bears watermelons and is native to tropical Africa but widely cultivated

As Slashfood points out, all of AP's examples are actually fruit - pumpkins, squash, cucumbers, and yes, watermelon. Whether you cook it like a vegetable or not, if it's got seeds, it's a fruit. It's one thing for AP to get this wrong, but another entirely to spend a paragraph going out of its way to make the wrong call. Yeesh.