[Sync] Fix bug where DeviceInfo is missing a backup timestamp

[Sync] Fix bug where DeviceInfo is missing a backup timestamp

Remove last_synced_time_ member variable from ProfileSyncService.  This
variable acted as a cache of the underlying pref.  However, it was not
properly cleared in ProfileSyncService::DisableForUser when the
associated pref was cleared.  This caused a bug where device info may
not have a backup timestamp.

BUG=427096
Committed: https://crrev.com/44d307099fc662e56b57c59f23214a85c2b206b2
Cr-Commit-Position: refs/heads/master@{#301481}

[maniscalco, 2014-10-27 19:05:50]

maniscalco@chromium.org changed reviewers:
+ zea@chromium.org

[maniscalco, 2014-10-27 19:05:51]

Nicolas, would you please review this change?

[Nicolas Zea, 2014-10-27 19:07:50]

LGTM!

[maniscalco, 2014-10-27 21:32:07]

On 2014/10/27 19:07:50, Nicolas Zea wrote:
> LGTM!

Thanks for the speedy review!

[maniscalco, 2014-10-27 21:32:15]

The CQ bit was checked by maniscalco@chromium.org

[commit-bot: I haz the power, 2014-10-27 21:34:18]

CQ is trying da patch. Follow status at
 https://chromium-cq-status.appspot.com/patch-status/660023003/40001

[commit-bot: I haz the power, 2014-10-27 23:34:17]

Committed patchset #3 (id:40001)

[commit-bot: I haz the power, 2014-10-27 23:34:59]

Patchset 3 (id:??) landed as
https://crrev.com/44d307099fc662e56b57c59f23214a85c2b206b2
Cr-Commit-Position: refs/heads/master@{#301481}