"Trademark law is unambiguous on the point that prior use of a mark in commerce always trumps (within the geographical area of such use) subsequent registration

"Trademark law is unambiguous on the point that prior use of a mark in commerce always trumps (within the geographical area of such use) subsequent registration of that mark by one whose actual use was later in time." I was under the distinct impression that trademark law was unique in that it was a form of intellectual property where being first didn't guarantee a victory. For example: If McDonalds (the Golden Arches) opens up a franchise location in a small mid-western town where a Scottish family had been running a business for the past 200 years, the Scottish family could be forced to change their name because McDonalds has greater brand recognition. If you can find something that will back up your understanding (or mine, because I can't find anything), I'd really like to see it.