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Otherwise, we might crash flakily on windows, as we might tear down
the Shell (WebContentsDelegate) before the callback to select a
filename has returned.

BUG=819739
R=battre@chromium.org

Change-Id: I09348f556ee10a9efae738b0ee2721c23641590a
Reviewed-on: https://chromium-review.googlesource.com/954944
Commit-Queue: Jochen Eisinger <jochen@chromium.org>
Reviewed-by: Dominic Battré <battre@chromium.org>
Cr-Commit-Position: refs/heads/master@{#541778}