I am very confused by this group, because they seem to completely misunderstand the situation. If anyone is wondering what the OP is talking about, take "Medical Residency Resources", remove the spaces, add a "www." to the front and a ".com" to the end and you'll find it.
They have a link to an ACGME petition. It's really quite funny, because what they are asking for is already completely legal.
They want to "End The ACGME’s Stranglehold on Medical Residency Funding!" Sorry to say, but the ACGME says nothing about funding residents and has no control of this at all. Feel free to review the ACGME Common Program Requirements, search for "funding" or "salary" and you'll find nothing. The ACGME does control the number of slots available in each program, but that's based on educational resources -- if I show I can accommodate more residents, they will increase my cap (assuming my other metrics are all good -- i.e. my resident or faculty survey doesn't show any problems).
If there was a practice in rural america that wanted a doc, it would be completely legal for them to fund a residency slot. The program would pay for all of the training costs of the resident, and in return the resident would sign a "return of service" contract with the practice. The program would need to have an approved slot open for this. This already happens -- some foreign governments fund slots in programs, and then the grads are required to return back.
Logistically it's a bit of a mess. But it would be possible for VC (or some other sort of funding) to pay for a resident's training costs, and then have the resident pay them back over time -- basically just like a mortgage. But this would need open, unfunded slots to work -- I don't know how many of those that there are, nor how many programs would be willing to do this. Personally it seems like a bad idea to me, although is really no different from taking out loans to pay for medical school.