the paternity testing I believe was done by licenced laboratory, and concerned the red puppies and their parents. The DM testing with inconsistent results was in a different dogs and as far as I know the results of simultaneous DM and paternity testing were not published yet.
The mistakes in DM testing might easily come from DNA contamination or from mixing of samples, as it is mostly done not in licenced lab, and incoming samples are not taken by a strict protocol. That's why the results are only partly official, there is no certificate. So mistakes can happen and sometimes do. DM test are also done by licenced lab (in that case the results of parents and offspring should be consistent).
Highly off-topic paragraph: The only official results of DNA tests you can get with samples being taken and labeled by a licenced veterinarian (who puts a stamp and signature on it, so should carry consequences if it is shown later that the samples were mixed up before coming to the lab), so that there is no question of their being taken from declared animal (that means the vet should check the chip or tattoo number against the passport or the pedigree). Then the sample goes with the copy of pedigree (proving the identity of the dog in question, and having the same chip or tattoo number!) to the certified lab which has to at all times keep track of the sample with proper labeling of all extracts etc, so that the results can be unquestionably traced back to the original sample and from it to the animal in question.
You can get results on any DNA samples which you send to a testing lab, but it only proves that the results were obtained from that sample. If you have no way to prove that the sample was for sure taken from that animal, than you don't have official results of that animal!
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