On a large, fully staffed, project team, under ideal situations, who would you expect to own the project timeline?
At the company I work for the Project Manager owns the timeline, but everyone on a project has access to it and is responsible for making sure their tasks are completed within the time slot allocated. Having the timeline in a shared location means that everyone can see task dependencies both upstream and downstream of their own pieces of the project, and give feedback to the PM when changes need to be made.
In short, everyone has access to the timeline, but if a change needs to be made it's the PM's responsibility. If the entire schedule is going to slip, then I'm sure the PM will get input from the business owners as well as from the project team members.
Its the project manager's responsibility to "own" it from an accountability standpoint.
Importantly, the PM also owns the expectations management that comes with managing the project timeline. This flows upstream to project sponsors and clients, downstream to team members and across the stream to accounting.
According to PMBOK the PM is the only person who owns Schedule (timeline, as you call it).