Any ruling by the chair can be overturned by a majority vote.
True that. It's basically "the Senate" sitting as a trial court. The senators are jury, judges, and advocates for one side or the other. They will do what is politically expedient, every time. Good thing conviction requires 2/3rds.
The Senate voted against an amendment that would require the Chief Justice of the United States to rule on motions to subpoena witnesses and documents.