From the website intransit.us :
Though NIH funded MSTP seats are meant for permenant residents and citizens of the United States, many MSTP funded schools have mechanisms which allow them to accept non-citizens. These funding mechanisms are usually institutionally or privately derived, and therefore, limited. An excellent international candidate should have no trouble being accepted to a program if one applies wisely. Furthermore, many schools do not have an official policy on international students, and handle them on a case-by-case basis. If you are very interested in a particular program, it would be worth contacting the administrator/director to see if the program has any 'wiggle room'.
Which I interpret as, it's actually more difficult. But maybe there are some international students who could speak to this better than I can.