It is more accurate than I realized.
I've found ten people in WikiTree who can trace all their ancestors back at least four generations to the same country and have a GEDmatch ID:
Today I discovered that GEDmatch's Oracle-4 attempts to pinpoint your [modern] ethnic group of origin. https://www.gedmatch.com/gedwiki/index.php?title=Admixture
Oracle-4 shows the three persons in WikiTree with all English ancestry as
1 Southwest_English @ 3.794286, 2 Southeast_English @ 3.947610
1 Southeast_English @ 2.674424, 2 Southwest_English @ 2.747479
1 Southeast_English @ 2.653272, 2 Southwest_English @ 3.738122
The one person with all Italian ancestry:
1 North_Italian @ 5.280625, 2 Tuscan @ 9.284982
The odd ones are the person with all Danish ancestry:
1 North_German @ 6.236578, 2 Swedish @ 6.555415, 3 Danish @ 6.688893
and the person with all German ancestry:
1 South_Dutch @ 2.905174, 2 West_German @ 3.139654, 3 French @ 7.970687
The others have old Family Finder GEDmatch IDs.