2) program of my interest has roughly half the faculty listed there without NIH-funding in this year (2011). Maybe they went into teaching more or got other funding than NIH (which I don't know what)... I have no idea.
I'm going to make the following controversial statement. As an MD/PhD student it would be really stupid to work for anyone other than an R01 or equivalently funded PI. The only exception is a brand new investigator with a large startup package and some funding who is applying for R01s and who everyone thinks will be successful. Though that is still a gamble.
There are unusual cases of well funded investigators from other sources, such as the HHMI grants, regional research grants, or large callobrative grants. Still, large career defining grants outside of the R01 essentially don't exist. This generates your job stability/tenure.
Now graduate school chairs might say, well you go get your own funding. We'll throw you a bone and let you spend a lot of time teaching for us and pay for you. But you need to be applying to the NIH, NSF, private grants, etc if you want to work with most of our professors. They will argue this is an essential part of graduate school, both teaching and fighting for money, as this will be the rest of your career as a PhD. Now this is BS for a few reasons as it applies to MD/PhDs, mostly because the MD is going to generate clinical revenue and is not going to generate revenue from teaching. In addition, even the MD/PhDs at big name MSTPs don't usually write grants, in part because the F30 (MD/PhD predoctoral) grant mechanism is so limited. So you can write grants for graduate school funding, but you're just eating up time. That makes more sense for the PhD student in their first year of grad school who plans on being in grad school for five or six years. You plan on being in grad school three or four years.
Now in a program like that it's hard to know how much cohesion there's going to be from the MD/PhD PD. There's really two options. The first is, the PD is going to say go do whatever the graduate school says. Go work for whoever you want. You're earning a "real" PhD, and that involves risk for funding/PIs moving during grad school and that involves spending a long time in grad school. I personally think that is a very weak PD, but they don't have to do much in this case and they keep the graduate programs happy.
The second option is to severely limit who you can work for. You will thus be looking at a small minority of well funded investigators who not only can support you but would be good mentors. And believe me, a big name researcher is often not a good mentor. Everyone is going to pissed off at this PD. The grad schools are going to be mad because the MD/PhD program is steering its students to certain labs, and the MD/PhD students don't really understand these issues and get pissed because the boss is telling them they can't do things.
But what I wonder is, if you go to program like Dartmouth, would your chance of receiving R01 and other types of grants later be "lower" because your program isn't NIH-funded?
No. Your goal is always to get to the next step in the ladder. Just as nobody looks at your high school performance when you apply to med school, nobody is going to look at your grad school performance when you apply for big grants. The goal now is to learn, think, and get yourself a strong residency so you can get yourself a strong fellowship so you can get yourself a strong faculty position so you can get yourself big grants. Get the idea? The real pitfall of going to a non-MSTP is not some stupid concept of "prestige". The real issue is whether they will be a strong MD/PhD PD to back you up, a strong MD/PhD mentoring system to walk you through these issues, and whether there will be a good choice of strong investigators who will get you where you want to go. If you end up taking forever and become a burnt out shell of yoru former self to get a PhD because your PI left, you couldn't sustain funding in your first lab, your PI used and abused you, you had bad advising and worked really hard towards things that didn't benefit your career, etc, then you will not use your PhD, you will run to a mostly clinical position, and your training will have failed itself, even if you do end up with a fancy piece of paper that says PHILOSOPHAE DOCTORIS or some crap.
In the end, if you feel the program has the right resources for you and then you finish respectably in about eight years with the residency you want, you will be in the same position as anyone else.