The short answer is yes.

All medical test including DNA testing can be wrong. That is why scientist speak of probative predictive value, false positive etc.
With DNA teasing becoming more common socially and legally, I think it will be helpful to know when a DNA test can get it wrong.

A human being who is a Chimera can fail a DNA test. A human Chimera caries two different DNA inside their body. Some Chimeras actually have body parts from a different human inside their body. They can also have two different blood groups.

We believe the most common reason for genetic chimerism in humans is the what is nicknamed the "Vanishing twin syndrome".... one twin dies in the womb and their DNA gets absorbed into the twin that survives. Other potential causes are miscarriage (babies DNA gets absorbed into the mother), bone marrow or organ transplant.

You can read about some human chimeras here [url][/url]http://pictorial.jezebel.com/one-person-two-sets-of-dna-the-strange-case-of-the-hu-1689290862

As genetic testing becomes more sophisticated, more human chimeras will be identified. We do not know how common human chimeras are because the test is not ready to be used for testing large populations. Because of the high rate of twin pregnancies amongst the yorubas, it is possible that they may have more human chimeras than other tribes.

However, the US just got it's first case of failed paternity test due to genetic chimerism [url][/url]http://www.buzzfeed.com/danvergano/failed-paternity-test-vanished-twin

Lydia Fairchild, a human chimera, was accused of welfare fraud when DNA test showed she was not the biological mother of her children.

Apologies for the spelling errors...

Hmmm this can cause alot of trauma cos most people believe DNA tests to be foolproof