Of course you probably would have gotten a better rate had you had your house paid off. Then again, back in 2007 many mortgage companies were pushing through lots of mortgages they should have at rates they didn't deserve, so maybe not. I mean the crazy approach to lending back then is part of what put us here. Lending to the recently bankrupt, not substantiating income, etc etc all got people into houses they shouldn't have been. But that is a totally different situation.
Of course you can't change out your loans then declare bankruptcy, that would indeed be fraud. However, if planned right it could certainly work. Downside is it requires some good planning and a serious handle on your finances. Most people that declare bankruptcy don't have either or get blindsided by some outrageous unexpected expenses (such as medical bills).