I agree. In this particular case, we're not dealing with a long-dead philosopher: we're dealing with the language of a thriving community. The question is, or should be, _what terms do they use_? In particular, what terms do they use when they're speaking English? (In Pennsylvania Dutch, I suspect they call it "Deutsch".) Certainly, the region is called the Pennsylvania Dutch Country, not the Pennsylvania German Country. Googling won't get you this one--the Amish avoid the Internet.
User Someone_else suggested a good compromise in this case; referring to the language as "Pennsylvania German" and to the people as "Pennsylvania Dutch". The articles could be split up if either treatment gets too long.
When dealing with the name of a people, it is proper to go by popularity alone. When dealing with a language (or, like Occam's Razor, a philosophical concept), the opinions of scholars must weigh more than the Google count alone.
Regards,
Erik