This might be related to code in chrome_toolbar_model_delegate.cc.  Example:

return !search::IsInstantNTP(GetActiveWebContents())

Michael, I think we want whatever signal hides the URL to come from ToolbarModel if possible, and if not that, we can override the "show URL" property with extra logic in our new ToolbarHelper class.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/2230cfaa7af10a8cf0aeae6c1e2262517f6ae7cf

commit 2230cfaa7af10a8cf0aeae6c1e2262517f6ae7cf
Author: Ian Vollick <vollick@chromium.org>
Date: Mon Jul 17 16:46:22 2017

[vr] Add e2e test for native UI

This should let us confirm our URL behavior on NTP and friends.
It also provides a convenient place to do more testing of
native UI in VR.

Bug:  738583 
Change-Id: I983016bdcef62ab83e0265929e7b00230a1a661f
Reviewed-on: https://chromium-review.googlesource.com/571948
Commit-Queue: Ian Vollick <vollick@chromium.org>
Reviewed-by: Yaron Friedman <yfriedman@chromium.org>
Reviewed-by: Tibor Goldschwendt <tiborg@chromium.org>
Reviewed-by: Michael Thiessen <mthiesse@chromium.org>
Cr-Commit-Position: refs/heads/master@{#487116}
[modify] https://crrev.com/2230cfaa7af10a8cf0aeae6c1e2262517f6ae7cf/chrome/android/BUILD.gn
[modify] https://crrev.com/2230cfaa7af10a8cf0aeae6c1e2262517f6ae7cf/chrome/android/java/src/org/chromium/chrome/browser/vr_shell/VrShell.java
[modify] https://crrev.com/2230cfaa7af10a8cf0aeae6c1e2262517f6ae7cf/chrome/android/java/src/org/chromium/chrome/browser/vr_shell/VrShellDelegate.java
[modify] https://crrev.com/2230cfaa7af10a8cf0aeae6c1e2262517f6ae7cf/chrome/android/java/src/org/chromium/chrome/browser/vr_shell/VrShellImpl.java
[add] https://crrev.com/2230cfaa7af10a8cf0aeae6c1e2262517f6ae7cf/chrome/android/javatests/src/org/chromium/chrome/browser/vr_shell/VrShellNativeUiTest.java
[modify] https://crrev.com/2230cfaa7af10a8cf0aeae6c1e2262517f6ae7cf/chrome/browser/android/vr_shell/vr_shell.cc
[modify] https://crrev.com/2230cfaa7af10a8cf0aeae6c1e2262517f6ae7cf/chrome/browser/android/vr_shell/vr_shell.h

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/3d1e1bdecc7d26bd8a9a45d1a79115874c7640cd

commit 3d1e1bdecc7d26bd8a9a45d1a79115874c7640cd
Author: Tibor Goldschwendt <tiborg@chromium.org>
Date: Tue Jul 18 04:10:31 2017

Don't show URL if there is no web content.

Bug:  738583 
Change-Id: Ib6fe7ab3eb136cc193333a2c198c431d31d4f58d
Reviewed-on: https://chromium-review.googlesource.com/568685
Reviewed-by: Ian Vollick <vollick@chromium.org>
Reviewed-by: Michael Thiessen <mthiesse@chromium.org>
Reviewed-by: Peter Kasting <pkasting@chromium.org>
Commit-Queue: Tibor Goldschwendt <tiborg@chromium.org>
Cr-Commit-Position: refs/heads/master@{#487383}
[modify] https://crrev.com/3d1e1bdecc7d26bd8a9a45d1a79115874c7640cd/chrome/android/javatests/src/org/chromium/chrome/browser/vr_shell/VrShellNativeUiTest.java
[modify] https://crrev.com/3d1e1bdecc7d26bd8a9a45d1a79115874c7640cd/chrome/browser/android/vr_shell/vr_shell.cc
[modify] https://crrev.com/3d1e1bdecc7d26bd8a9a45d1a79115874c7640cd/chrome/browser/android/vr_shell/vr_shell.h
[modify] https://crrev.com/3d1e1bdecc7d26bd8a9a45d1a79115874c7640cd/chrome/browser/ui/toolbar/chrome_toolbar_model_delegate.h

Looks like this is fixed! Please reopen if I've got that wrong.

 Issue 691576  has been merged into this issue.