I agree that DNA cannot lie, but how likely is this senario, which has actually happened? I have an uncommon surname, shared so far as I can calculate from a variety of sources with approx 1200 males in the world. I took a Y chromosome DNA test 37 marker from FTDNA last February. So far I have found the following, I share 36/37 markers,together with haplotype, with a person in western Canada, whose ancestors were in the same general area of Lincolnshire as mine between 100 and 215 years ago, so a liason between the two families is quite feasible, however I and he have so far been unable to find it.
More pertinently I share 33/37 markers and a surname, but a different haplotype with a man in Worcestershire. We have separately produced possible trees which suggest a common ancestor in Wiltshire pre 1600AD, the haplotype difference suggests we have been separated for over 20,000 years, long before surnames. In view of the scarcity of the surname I think an error by the company is more likely than a co-incidence.