I am going to use ancestry DNA as an example and talk a bit later about DNA testing for more up to date types of tests.
DNA testing can’t give us real answers to profound questions such as an explanation of why we are the way we are. Genetic tests can be useful by revealing your ancestry (especially immediate family members). Still, a DNA test cannot tell you much about your history, culture, or how it should influence your identity. Don’t read too much into it.
A DNA test determining your ancestry can connect you to the past, but on a superficial level only. More usefully, DNA tests are great for indicating your propensity for specific conditions such as how you can lose weight, prevent aging and what type of athlete you are.
There have also been some online articles about DNA tests yielding different results from different genetics companies. A closer look at these articles, however, will reveal that the differences were only minuscule.
One author, for example, found that his DNA test revealed that he was Ashkenazi Jewish, but the Ashkenazi percentage ranged from 85% to 93%. Each company gave him a different figure. He was Ashkenazi Jewish but with differing percentages with a varied range of only 8%.
So again the answer appears to be Yes, DNA test can be wrong. But the validity and accuracy of a test depends on the lab and how they preform the testing.