VERSION
Chrome Version:  64.0.3282.24 beta
Operating System: Chrome OS 64.0.3282.24 beta

REPRODUCTION CASE
Set the following policies in Google Admin
Policy Bypass - Device Management > Chrome > User Settings > Security > Incognito Mode > Disallow ingcognito mode 
Policy Bypass - Device Management > Chrome > User Settings > User Experience > Developer Tools > Never allow use of built-in developer tools


Restart the Chromebook.
Log in and open up Chrome.
Go to Chrome://inspect and choose the Other tab.
Click inspect under chrome://oobe/lock.  
Note: chrome://oobe/lock only appears once after reboot and sometimes takes time to appear.
This opens the Dev Tools window.
Click "Application" from the Dev Tools window.
Choose Manifest.
Click "Read more about the web manifest"
This force opens https://developers.google.com/web/fundamentals/web-app-manifest/?utm_source=decode in incognito mode.

If you close the incognito window it cannot be reopened by this process until the chromebook is restarted.

We're happy here at RSU1 to help you test a fix.
Credit to emma.boynton@rsu1.org for discovering the original flaw.