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This CL removes uses of set_owned_by_client in the Global Media
Controls code.

Bug: 1009708
Change-Id: I08a0c49310b356a225a92f5522189f3e69621524
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1885499Reviewed-by: Scott Violet <sky@chromium.org>
Commit-Queue: Tommy Steimel <steimel@chromium.org>
Cr-Commit-Position: refs/heads/master@{#710499}