While I am also skeptical, there are watermelon-like species native to the southwest, for example calabazilla (Cucurbita foetidissima) that could have been the

While I am also skeptical, there are watermelon-like species native to the southwest, for example calabazilla (Cucurbita foetidissima) that could have been the starting point for selective breeding. Native Americans selectively bred other cucurbits, so it's not entirely unreasonable to think they could have created a watermelon-like fruit. Comparing DNA would give you the answer, but you could also look at morphological characteristics. For example, true watermelon (Citrullus lantanus) has highly lobed leaves, while based on one of the pictures in the article, this "watermelon" species does not. Potential wild relatives in the southwest also don't tend to have lobed leaves, for what it is worth.