Thanks for your response.
The device is a ZTE Z752C. It's running Android 4.4.4.
NMS shows the location of the unsecured network I have supposedly connected to. It's in my immediate neighborhood, about a quarter mile away. The SSID is AH-GUEST, which sounds like someone's guest network. I don't know how accurate the location is, but I have gone to that location and do not detect that SSID.
Yes, I'm the only user of the device. The phone has always been on my person or in my locked home or car. I make a habit of locking it when I stop using it, and at any rate it is set to lock after only one minute. NMS is set to wipe the phone if more than 20 tries are made to unlock it. So I would really have to be pretty paranoid to believe somebody else was using my phone.
I'm also guessing that the supposed connection has occurred since I installed NMS, which was only a couple of weeks ago. So my memory of that period is pretty good.
As I said in my original post, I have never explicitly connected to any WiFi other than my home WiFi. If I had somehow connected by accident, I believe it should show up under my WiFi settings unless I somehow also accidentally deleted the connection from my settings.
I'm still speculating that there may be some sort of automated connection that Android may be making. Perhaps the functionality is limited, but still triggers the NMS warning.