Jumping back in to the conversation, I wasn't able to get a direct reply from HealthGene on how they test for the presence of the piebald gene in Biewers and Parti Yorkshire Terriers, but HealthGene did refer me to Dr. Schmutz's 2009 paper on MITF and white spotting in dogs, and I found the answer buried in Table 2 of that paper. Here is the link to the paper:
MITF and White Spotting in Dogs: A Population Study
Table 2 lists the genotypes of 151 dogs from breeds in which individuals with random spotting were homozygous for the SINE insertion in the MITF gene. Two Biewers tested homozygous for the SINE insertion.
According to Dr. Schmutz's paper:
The SINE insertion 5′ of MITF-M first described by Karlsson et al. (2007) was associated with white markings in many and diverse breeds in this study, suggesting that it is an “old” mutation. There is considerable debate about the age of particular breeds. However, the Chinese Shar-Pei, Akita, and other Asian dogs are typically considered to be among the oldest breeds (Parker et al. 2004). The SINE insertion has been found in individuals with white markings in these breeds.
Since breed standard Yorkshire Terriers are solid colored and do not carry the piebald allele (the MITF gene with the SINE insertion), it had to have been bred in from some other dog breed to create the Biewer. Case closed.