When I hear "living paycheck to paycheck" I think it means your recurring expenses (rent, utilities, food, etc.) consume all your income every month and you have nothing left to save. No savings. No investments. No 401K. If you don't get your next paycheck you can't pay the rent.
I think your definition is completely reasonable, but it's not how people answer the question (again, based on reading the report, which has a lot more detail.)
