Is it the case then that any school receiving any funding from NIH for MD-PhD training is classified as an MSTP?
Yes, as long as the money is from the Medical Scientist Training Program grant provided by the NIGMS. As you read, realize that this is more of a prestige thing for the medical school then a revenue generator (more like money sink).
Does anyone know how many spots in MSTPs are actually NIH funded or if a student may be better off in a program that is NIH funded for a greater percentage of students?
For the first question, it depends on the program. I would strongly disagree with the second question you pose. If anything, a program that devotes more money for the program from the medical school indicates to me that the school itself is dedicated to producing MSTPs, rather than just letting them train there. That's just my personal bias.
http://drslounge.studentdoctor.net/showthread.php?t=263411
See this thread for a list of MSTP funding for 2004. You could compare this to the size of different programs and get a sense of what percentage of the program's funds come from the MSTP grant. For Penn for example they list 50 students and they have around 150 students fully funded in the program. Note that the NIGMS doesn't cover all of the expenses for a given student (i.e. their tuition and salary allotments are less than what the schools need/give). So at most the NIGMS provides 33% of the MSTP budget at UPenn, but my guess is that it's more like half of that. Pitt told us when I interviewed there 5 years ago that the MSTP grant only provides ~20% of their budget.
Keep in mind however that about half of those students are in graduate school, and those students in graduate school are the responsibility of other, usually NIH grants.
Are the bigger programs (WashU and Penn) primarily funded by NIH or by the schools themselves? or from where else does the money come?
Both. The majority of the MSTP money not coming from the NIGMS is true of most (all?) programs, even ones that are not as large. Most schools chip in the remaining money from private funding/endowment/other grants (such as PIs funding the PhD phase).
For students currently in programs, how much does funding matter?
Where the funding comes from? I don't know or care where mine came from. It's a non-issue. You can write your own grant, and different schools/PIs encourage this to different degrees. Usually it's simply for the experience/prestige of getting your own grant than for the actual need of money.