How can unauthorized movie purchases be made on my 1st generation Apple TV? In the last 6 months, two movies have shown up as purchased on my 1st Generation Apple TV, but neither I nor my wife have purchased them.

The first time this happened, I thought perhaps it had been done accidentally by my wife previewing a movie, then accidentally hitting the purchase button.

The second time this happened was last night when we were watching Monday Night Football. We were both sitting on the sofa and the AppleTV was NOT accessed by us. 

Our ATV1 is a refurbished 160GB AppleTV purchased directly from Apple with the latest software version [3.0.2]. I run ethernet from a Netgear WNDR-3700 router to the AppleTV. Password has been changed from default on the router. I have disabled the guest networks (yes this router has two guest networks) on the router, but do run WiFi for the windows computers and three local Apple devices (2 phones, 1 iPad 2nd gen).

The first time this happened, I enabled two-step verification on my Apple ID. Strangely, I get the two-step challenge ONLY when I sign-in from my Chrome Browser on the AppleID site, [ https://appleid.apple.com/account/home ].

Can anyone tell me how unauthorized purchases could be made on my AppleTV without my knowledge? 

Further, can anyone tell me how to lock down my network and 1st gen  AppleTV so that unauthorized purchases can't be made?
I know this is a month old, but check your ir remote. My Fios remote is programmed to control my Apple TV. If the Apple TV is on, the remote may be triggering the purchases when you use the up, down and menu keys on it. Since you are watching another show through a different input, you won't even notice it until you get the bill. 
Reprogram the universal remote or tuck the Apple TV where the IR signal can't SE it.