Here's what I'm seeing now:
I added the album on 4/22/2017 at 2:34 PM
Jóhann Jóhannsson – Free The Mindhttps://www.discogs.com/J
Today, I shut down MusicBee and restarted it. I now see:
Modified: 4/22/2017 2:34 PM
Added: 4/24/2017 1:43 AM
I played one track, shut MusicBee down and restarted -- but this time, it didn't change the "Added" date, and kept the right play count and time.
I had also added an Ólafur Arnalds track at about the same time and played it right away, but nothing seems to have changed on it unusually,
So something did clearly get weird on the Jóhannsson (since, clearly, I couldn't have modified it before I added it), but it's not behaving consistently.
(The most maddening thing is when something fails to fail as expected