I have quite a few friends who are doing MD/PhD's in bioinformatics at a number of different schools (Gerogia Tech, BCM, Case Western).
At least anecdotaly, they tell me they think they will graduate faster because they don't have to "wait for data." They say that is the trend. Additionally, one of my friends just does his work from home, the coffee shop, wherever and just checks in with his PI once a week and goes to lab meetings, J-clubs, etc. So I think there are some things about doing a computational PhD that make it a little different and maybe for some people more enjoyable than a traditional wet-lab project.
Also, keep in mind that lots of different departments at most major medical research institutions have people doing bioinformatics research -- namely bioengineering, genetics, biophysics, and structural biology. Just because the program isn't called "Bioinformatics" doesn't mean that there aren't a lot of people doing that work.