That’s a very clever plan (having your parents acting as a mortgage lender to bypass the scrutiny of an institutional lender). There is a small “penalty” for doing this:
Since the house will change hands twice, there are additional transaction fees. But, since the sale from your parents to you is a “private party sale” (i.e. no broker/realtor commisions), the fees should be much less.
Your situation is a “special case” because not everyone who is upside down has parents who have the financial resources to buy a house with cash.