I don't really think it will hurt to say that you will borrow to pay for med school. There really should not be any preference since either way they will get their money.
I think if you can pay for four years of med school out of pocket you should. I think admissions would be a little leary of that since I am sure it doesnt happen often.
They may be afraid that you won't be able to come up with the money year after year. They would be more secure if you said I will pay through loans because they know they will get there money. It has to have some baring on admissions because that was one of my interview questions.
If you have a choice, I'd say take the loans. At least if you can deffer the payment until you graduate. Especially if you can defer it until you finish residency.
$80,000 ($20,00 each of the first four years) at 10% (invested in the market) will yield around $55,000 after 7 years. That will put a BIG dent in your loan.