Yes, Carol, your thinking is wrong.
They're using the x in the botanical name to stand for Rhododendron hybrid, meaning that it isn't an unadulterated species rhododendron. In contrast, we don't include the "x" or the word "hybrid" in the botanical names in our database.
If it were a parentage formula, it would say:
unnamed Rhododendron x Nome
If it were a hybrid of Nome and another unnamed Rhododendron, it would have a different cultivar name in single quotes.