The issue that was resolved on this thread has raised its ugly head again: https://premium.wpmudev.org/forums/topic/membership-communications-not-on-schedule#post-388248
My test account started getting the communications again (day 0, and day 3). This is long after the account was set up. The test user shouldn't be receiving any communications at this time.
I can only guess that other users are getting the same erroneous emails, however, there isn't any way to track them in the dashboard.