[Doodle] Move image fetching from LogoBridge to DoodleService

This will allow us to transparently implement different image fetching
logic (e.g. inlining the image data into the doodle config).
And this logic doesn't really belong in the bridge anyway.

BUG=719513

Review-Url: https://codereview.chromium.org/2886443002
Cr-Commit-Position: refs/heads/master@{#472732}
10 files changed