To answer your question..I don't think they'll admit someone on the basis of how they will pay for their tuition.
As far as my school goes, the average cost for in-state first year is $26,000. Unless you have $26,000 tucked away someplace, you're gonna have to take loans. About 97% of students at my school take some sort of loan, whether it is federally funded or private. I would first worry about whether you get into the school that you want to first, then you can look into financial options. Its not that most schools "want" you to take loans, its that most schools anticipate that you'll take out a loan. Just compare this to buying a house or a car. Do most people really have that much money tucked away someplace for a $20,000 car or a $200,000 home?? No. They get loans. Same is true for a medical education. I hope this addresses your question....