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Renamed to avoid all the fun-and-games of overload resolution with template functions.

Part of the overall effort to eliminate the need for and eventual removal of set_owned_by_client().

Bug: 1044687
Change-Id: I4f728af6e17b3c6c804db7eda58f0fb6d426d5f9
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2068878
Commit-Queue: Allen Bauer <kylixrd@chromium.org>
Reviewed-by: Peter Kasting <pkasting@chromium.org>
Cr-Commit-Position: refs/heads/master@{#746505}