Yes, you are correct the XML is looking for the XML first, but both Google Webmaster discussions and Yoast both state that the spiders will crawl your sitemap to help get a better idea of how your site information is interconnected.
See https://yoast.com/html-sitemap-wordpress/
I would also like to link the sitemap to the 404 page not found page as a convenience.
In any case, I would still like to know where your sitemap.php is putting its file and how to view it and how to use it.
Thanks,
George