Ok, just learned something new: it seems like Wilhelm indeed preferred the titel King of Prussia to the title Emperor.
Strange, I was convinced that it had to do with the principle that the "King of Prussia" was in his understanding "by the grace of God", while any Emperor title would always have the connotation as being granted (or at least approved) by the princes of the other German states, and tehreby by a lesser authority than God. Maybe a hypothesis made up by my history teacher in highschool?