Isn't public debt the debt of the public?

The art in Detroit cannot be sold because it is owned by the public. Considering that the debt is that of the public, it seems that something is logically wrong. Detroit is a city of "people", and those "people" voted for, or leveraged the use of money that caused the debt. Regardless of what the lawyers *think* the answer is, the correct answer is that the people owe on the debt.