I know, it sounds too good to be true, but it happens. I personally have helped many families do just that. The secret is in knowing how to structure your offer and where to go for the money. In one case, my investor buyer was paid $1,100 at closing, then collected rent of $1,500 on the following friday. A single family home buyer received their returned rent deposit of $700 from their landlord, $725 at the closing for their home and didn't make a mortgage payment for nearly 45 days. Their new loan payment was less than they had been paying in rent.
I know, you think this is trickery, or predatory lending, right? Wrong. Both of these buyers secured 30 year fixed rate financing for the properties. We simply talked to the right lenders, those with community loan products that had low costs and low interest rates. Then the lender and I formulated our buying strategy, the buyer located the property and we executed the plan. Using the right loan and additional funds either from the seller, in the form of points and closing costs help, or from a community down payment assistance program, not the charity programs that are getting all the heat, we coverd the balance of the expenses. Even under FHA guidelines the buyer can walk away with cash to them as long as it doesn't exceed the amount already invested plus the tax credit from the seller.
Experience makes the difference. With a great agent and a great lender comes a great experience. For help identifying the appropriate program in your area, contact a good mortgage originator at a local bank or savings and loan and a great Real Estate professional. Don't know one, send me a note and I'll give it the old college try.