Thanks for the link, Matthew, but unfortunately that blog discusses how to add a basemap that does have labels. As I noted in my initial post, many people have already suggested what it does with respect to not including the reference layer, but that was not what I was looking for.
So, to anyone who's looking for a basemap with no labels ("no, really no labels"), you can skip the blog post above. Russell Robers response about Vector Basemaps actually delivered.
Cheers,
jtm