My two cents would be that... no, it's not RIGGED against foreigners BUT it is much more difficult for them to get into a US med school. Think about it, most US MD schools are there because of a need of the local population for physicians. It's true that med school graduates go to other states, BUT the fact remains that they usually stay domestic. Why should a US med school invest all that time and money training a foreign student when the chance of them moving back to their own country after their residency is high? (higher than a US citizen anyway). It's roughly the same logic that public schools have a heavy preference for in-state residents. There also the chance that the foreign student might not finish due to financial (no access to federal aid) or legal (that's why they require at LEAST a permanent residency status) reasons that are usually not a problem for citizens.
However, OP, in your case, I don't think it's worth any worry... A US citizen is a US citizen (no matter what the road to it was).