How might the role of product owner go against the idea of open source, or work for it?

Question

On a related questions about "Finding and/or becoming an open source product owner" -- the first comment to the question itself was "the idea of a product owner goes against the idea of open source."

• Is this true, and if so, why?
• If not, what circumstances and/or context would it make sense for open source project to have a product owner role?

I've attempt to find an example of this role at Mozilla.org -- but I've had no luck so far.

(Just to be clear, I'm talking about a volunteer role, not a paid position at a non-profit.)