You're correct in saying that they would all be equivalent, but there are still 3 individual O atoms that can each have the double bond at some point in the ground state. Therefore, you would have 3 ground state resonance structures despite the fact that they're all equivalent.
I'm not sure if this helps, but think of benzene - it's also a symmetrical molecule that has many ground state resonance structures that are essentially identical, but they still each count as an individual resonance structure.