A 501(c)3 does not have stock, and upon dissolution the assets can only go to another 501(c)3. So, it is not owned in the sense that the members are stockholders or that it works in their financial interest, as a for-profit would.

However, I assert that the members own the organization in that it is responsible to them. And thus the officers must be as well.

For some organizations this is not appropriate, and it is chosen, upon formation, to not have members other than the officers. There are also non-profits which only have "associate members", who do not have voting privileges. Different choices were made for AMSAT, and they are here: https://www.amsat.org/articles-of-incorporation/