"Phone may be monitored" I'm seeing this message is because I installed a device owner, right?  (Note that I'm talking about a "device owner" in the sense of a special device administrator app, not the first user in a multi-user setup. Thanks to Izzy for drawing my attention to the possible ambiguity.)



This is Android 6.  I never saw this message on different device running Android 5 with the same device owner installed.

The device owner must be configured immediately after a factory reset, before setting up a user account.  I could factory reset the device and see if the message goes away, but I'm hoping to avoid that since I've already set up a bunch of other things.
This message is shown when a device owner is set.

I bit the bullet and reset my device.  It only cost me a few hours of setup.  The "Phone may be monitored" message appeared when I ran the ADB shell command dpm set-device-owner.