The most interesting part of this is that they are looking at mitochondrial DNA which is maternally inherited. People generally associate their ancestry to their surname and that of their antecendents which is paternally inherited. It would be very hard to look at non-mitochondrial DNA and determine origin as this gets swapped around so much.
So the authorities know that someone with the name of Mbere has or is likely to have Kenyan ancestry. They may be 1099511627775 parts in 1099511627776 Kenyan yet when tested it might be conclusively determined that the person comes from a Somali region where Al Qaeda is active all because someone went on holiday 1000 years ago. If its your job to determine suitability then this alone is probably grounds to send them back home.
As Kurt Vonnegut wrote, "There is nothing funny about national security. Nothing funny at all."