If we have one allele, only our external body is black, if we have two alleles, both our external body and our internal body is black.
As @A. B. and others have pointed out, due to the dominant nature of this gene, the protagonist’s parents would have each had to possess one allele, which they passed on to their offspring. If neither expresses black skin, this is hardly a plausible genetic condition.
Several solutions to this conundrum:
1. Switch the pattern of dominance.
If a person has one allele, only their internal organs are black. If they have two alleles, both their external body and their internal body are black.
This is, in my opinion, the easiest solution. Both Melanie’s parents have one allele of the gene. However, since this only causes internal organs to be black, neither of them express black skin. They may not even know that their organs are black. This allele could have been passed through her European ancestors for generations before she received two alleles, expressing not just the internal phenotype but the external black skin as well.
2. Regulation of gene expression.
As I suggested in the comments, gene expression could explain this discrepancy. Leave the alleles as is. Both Melanie’s parents possessed one allele of the trait, but it was not expressed. There are a number of genes which regulate melanogenesis and melanocyte differentiation, any of which may be turned off. In Melanie, these genes were turned on (could be due to any number of reasons), so she expressed the phenotype while her parents didn’t.
3. Environmental factors were involved.
The mutation was not inherited from her parents, but was caused by an environmental trigger such as pollution. This is in fact a plausible explanation for spontaneous generation of melanism.
Industrial melanism is an evolutionary effect prominent in several arthropods, where dark pigmentation (melanism) has evolved in an environment affected by industrial pollution, including sulphur dioxide gas and dark soot deposits.
Of course, as @Pelinore pointed out, the likelihood of this mutation randomly occurring twice, to mutate both alleles, is considerably less likely than one mutation. If you want to stick to your incomplete dominance explanation (and not complete dominance, in which one allele is sufficient to express the mutation), this explanation may not be plausible.