I believe ContentFaviconDriverTest.ReloadBypassingCache, as well as a new browser test I had to write (https://crrev.com/c/849292) both fail with the network service enabled for the same reason. Some sub-resource requests seem impossible to observe in browser tests with the network service enabled.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/21f3ea1fe1b1c08444019304cddba45c7c56755d

commit 21f3ea1fe1b1c08444019304cddba45c7c56755d
Author: John Abd-El-Malek <jam@chromium.org>
Date: Sat Mar 03 00:53:12 2018

Remove content_browsertests filter entries for network service for tests that have equivalents.

Bug:  787614 
Cq-Include-Trybots: master.tryserver.chromium.linux:linux_mojo
Change-Id: Ib78db05aabb5502977a8b08e2aee72a8481ca572
Reviewed-on: https://chromium-review.googlesource.com/946851
Reviewed-by: Chong Zhang <chongz@chromium.org>
Commit-Queue: John Abd-El-Malek <jam@chromium.org>
Cr-Commit-Position: refs/heads/master@{#540700}
[modify] https://crrev.com/21f3ea1fe1b1c08444019304cddba45c7c56755d/content/browser/loader/resource_dispatcher_host_browsertest.cc
[modify] https://crrev.com/21f3ea1fe1b1c08444019304cddba45c7c56755d/testing/buildbot/filters/mojo.fyi.network_content_browsertests.filter

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/aa4cb5fd6fa9c23d6f63e1376c7710c6dc17f653

commit aa4cb5fd6fa9c23d6f63e1376c7710c6dc17f653
Author: Jay Civelli <jcivelli@google.com>
Date: Thu Mar 08 23:20:56 2018

Fix for the ContentFaviconDriverTest test with the network service

Fixes the ContentFaviconDriverTest browser tests with the network
service by switching to using a URLLoaderInterceptor instead of the
URLRequestDispatcherHost.

Bug:  787614 
Cq-Include-Trybots: master.tryserver.chromium.linux:linux_mojo
Change-Id: Ifc04f6b8c85461f4974a8f6dd11b27e1beeef188
Reviewed-on: https://chromium-review.googlesource.com/955892
Reviewed-by: John Abd-El-Malek <jam@chromium.org>
Commit-Queue: Jay Civelli <jcivelli@chromium.org>
Cr-Commit-Position: refs/heads/master@{#541926}
[modify] https://crrev.com/aa4cb5fd6fa9c23d6f63e1376c7710c6dc17f653/chrome/browser/favicon/content_favicon_driver_browsertest.cc
[modify] https://crrev.com/aa4cb5fd6fa9c23d6f63e1376c7710c6dc17f653/testing/buildbot/filters/mojo.fyi.network_browser_tests.filter

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/6329dc2c31e86a1a4fcf58b3b1dcfec308ea077b

commit 6329dc2c31e86a1a4fcf58b3b1dcfec308ea077b
Author: John Abd-El-Malek <jam@chromium.org>
Date: Wed Apr 25 17:48:15 2018

Skip ThrottlesAddedExactlyOnceTo*Downloads tests with the network service.

These tests don't apply to the network service code path because
1) ResourceThrottles aren't used
2) Downloads go through a different path (interception of the URLLoader in NavigationRequest) that make the bug for these tests not possible

Bug:  787614 
Cq-Include-Trybots: master.tryserver.chromium.linux:linux_mojo
Change-Id: Ia3d620540801d26344fb8453228e911a2c629c10
Reviewed-on: https://chromium-review.googlesource.com/1028364
Reviewed-by: Matt Menke <mmenke@chromium.org>
Commit-Queue: John Abd-El-Malek <jam@chromium.org>
Cr-Commit-Position: refs/heads/master@{#553636}
[modify] https://crrev.com/6329dc2c31e86a1a4fcf58b3b1dcfec308ea077b/chrome/browser/loader/chrome_resource_dispatcher_host_delegate_browsertest.cc
[modify] https://crrev.com/6329dc2c31e86a1a4fcf58b3b1dcfec308ea077b/testing/buildbot/filters/mojo.fyi.network_browser_tests.filter

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/7e8aa6ab55116627ab54fb74bbedc866967a4722

commit 7e8aa6ab55116627ab54fb74bbedc866967a4722
Author: John Abd-El-Malek <jam@chromium.org>
Date: Wed Apr 25 20:21:43 2018

Enable a bunch of loading tests at the content layer with network service.

Eventually these tests should be renamed to not be specific to ResourceDispatcherHost.

Bug:  787614 
Cq-Include-Trybots: master.tryserver.chromium.linux:linux_mojo
Change-Id: I5cd54463f2bf296f58bbea40b0058fa802f35d13
Reviewed-on: https://chromium-review.googlesource.com/1026703
Commit-Queue: John Abd-El-Malek <jam@chromium.org>
Reviewed-by: Matt Menke <mmenke@chromium.org>
Cr-Commit-Position: refs/heads/master@{#553717}
[delete] https://crrev.com/4177bddffd6f1188254c499ca46ad3cc6a0f63d3/chrome/test/data/redirect-to-title2.html
[delete] https://crrev.com/4177bddffd6f1188254c499ca46ad3cc6a0f63d3/chrome/test/data/redirect-to-title2.html.mock-http-headers
[modify] https://crrev.com/7e8aa6ab55116627ab54fb74bbedc866967a4722/content/browser/loader/resource_dispatcher_host_browsertest.cc
[modify] https://crrev.com/7e8aa6ab55116627ab54fb74bbedc866967a4722/content/test/data/cross-origin-redirect-blocked.html
[modify] https://crrev.com/7e8aa6ab55116627ab54fb74bbedc866967a4722/testing/buildbot/filters/mojo.fyi.network_content_browsertests.filter

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/688321299f94e467ceea0b59ff49ba14615e8494

commit 688321299f94e467ceea0b59ff49ba14615e8494
Author: John Abd-El-Malek <jam@chromium.org>
Date: Wed Apr 25 22:32:22 2018

Rename ResourceDispatcherHostBrowserTest to LoaderBrowserTest since these tests aren't specific to RDH.

This is a follow-up to r553717.

Bug:  787614 
Cq-Include-Trybots: master.tryserver.chromium.linux:linux_mojo
Change-Id: Id0fc9c7e8314cfb97ca499b9161471f9850d3f9a
Reviewed-on: https://chromium-review.googlesource.com/1028520
Commit-Queue: John Abd-El-Malek <jam@chromium.org>
Reviewed-by: Matt Menke <mmenke@chromium.org>
Cr-Commit-Position: refs/heads/master@{#553796}
[rename] https://crrev.com/688321299f94e467ceea0b59ff49ba14615e8494/content/browser/loader/loader_browsertest.cc
[modify] https://crrev.com/688321299f94e467ceea0b59ff49ba14615e8494/content/test/BUILD.gn
[modify] https://crrev.com/688321299f94e467ceea0b59ff49ba14615e8494/testing/buildbot/filters/mojo.fyi.network_content_browsertests.filter
[modify] https://crrev.com/688321299f94e467ceea0b59ff49ba14615e8494/testing/buildbot/filters/site-per-process.content_browsertests.filter