It would be interesting to know how many markers they used in the analysis. Since the results are exactly 25-75, it could have been as few as 4 markers (I doubt that though).
The Ancestry interpretation is the most straightforward, but many other lineages could also explain the results, such as:
parent A: 12.5% coonhound; 87.5% foxhound
parent B: 37.5% coonhound; 62.5% foxhound
Knowledge of the genetics of one parent would constrain the likely genetics of the other, but not entirely.
The general rule is to add up the percentages of the parents and then divide them by 2 to get the percentages of the offspring.
Or working backwards, in this case, to go from the offspring to the combined genetic percentages of the parents:
25% coonhound x 2 = 50%; 75% foxhound x 2 = 150%
Any combination of parental genetics that would equal 50% coonhound and 150% foxhound would work in this case.
However, these would not be exact calculations, since the recombination (crossovers) and the sorting of chromosomes are both random and would affect the exact parental source a progeny would inherit from each parent in each generation. Taking advantages of these random effects is the basis of genetic tricks, such as marker-assisted breeding techniques, used for things like speeding up crossing a particular gene into an inbred genetic background by several generations. Parents with the highest or lowest percentages of a particular background are selected for breeding, using molecular techniques, in each generation.
Here is an example.
Thus, there are many possible ways to trade off one percentage for the other and an even wider array of parental percentages could, through the random effects, give the results described above.