Depends where you are. The bank often does hold the title, or at the very least hold power over the home owner. Which of those two it is varies by jurisdiction.
For example, I live in a state (Florida if it isn't obvious by my screen name) that does "lien theory", where the borrow retains the title, but other states and countries have "title theory", where the bank holds it. However, if I have a mortgage I may still retain the title, but the bank can force me to have homeowners insurance (thus power and influence over decisions I make about my home).
So to the point of state funded or state owned, it really is semantics, as the state will get a lot of say in things.
Also, state funded, if that's how you choose to think of it, effectively means a loan (i.e., DEBT) from the state.