Did you include a reference to the esri.css file? This requirement was added to the JS API fairly recently, and if you omit it the results look like what is show in your screenshot.
I would double-check that you've included a <link> tag to bring in esri.css and make sure it's being loaded via your browser's dev tools. That seems to be the most likely explanation for the issue you're seeing.
I put together a version of their "nested" sample and it works. It's attached as a .zip file.
Edit: You also said "WMS" but the screen shot looks like it's showing the standard ArcGIS Online Streets basemap. Did you mean tiled service? I used the streets tiled service in my example.