You're right about who is causing the damage etc. but the 'commons' does not refer to the people; it refers to the shared resource. So a public park is the commons. And when it gets polluted with plastic rubbish etc. because externalities are not internalized that's a tragedy of the commons.

The fallacy in "the tragedy of the commons" is that there's something inherent in having a shared resource that dooms the shared resource. At least this is the popular understanding. And I'll add that if we look at shared resources both with more breadth -- e.g. across history and cultures -- and in more depth -- e.g. cross-analysis, they come out looking much more successful than you'd think.

Thanks for both teaching me and not losing the forest for the trees of my point.