This built-in access level has been designed to give a user some broad powers within a project s/he is part of, much the same as a project manager in life normally enjoys in relation to the project s/he owns. The access level enables such a user (project owner, for ease of reference) to add projects, add, view, or edit activities, view and edit time logs of her own and other project members’, view and manage project members and assignees, etc.
"Nominal" vs. "actual" project owner
It is important to note that the built-in 'Project owner' access level is only a representative of a group of access levels that set aside a user from other users in terms of level of access within the projects they are part of. Project owners, in general and rightly so, have the highest level of access to their projects. It goes without saying. Any access level consists of permissions. And the permission that makes project owner distinct from lower access project members is "Manage members".
Accordingly, if you modify a member's access level so that it has this permission enabled, the member, de facto, becomes a project owner, too. Birdview treats such access levels as equal to project owner's. Accordingly, if you want to filter out projects by project owners, the resulting list will include members who nominally may not be project owners, but who are by virtue of their treat-as-project-manager access level.