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Revert of Cleanup: Remove base/file_util.h. Convert remaining references. (patchset #1 id:1 of https://codereview.chromium.org/568873004/)

Reason for revert:
Broke some internal builds. Need to give them a chance to fix their builds.

Original issue's description:
> Cleanup: Remove base/file_util.h. Convert remaining references.
>
> TBR=brettw@chromium.org
>
> Committed: https://crrev.com/6d63c4898c2da5a286d01f80229baeb914f99f18
> Cr-Commit-Position: refs/heads/master@{#294729}

TBR=brettw@chromium.org
NOTREECHECKS=true
NOTRY=true

Review URL: https://codereview.chromium.org/565803006

Cr-Commit-Position: refs/heads/master@{#294755}