It's not always the case, but there are clear areas of overlapping research and if there's a compelling need to meet the public need in one area, then the others are likely as well.

With that said, many recent private professional schools are opening in a for-profit structure. BYU's approach sounds non-traditional enough that it may not overlap into those other graduate areas. And, in all honesty, while med students and research can have a strong international effect, the same would not likely be true for dental students and pharm students. If BYU were to open those schools, they would be instantly full of qualified applicants, but those grads would likely continue to be concentrated in the western US.