How is someone able to pair their Arc Touch Mouse with my Macbook Pro?

I had this happen a few times now and it's both annoying me and scaring me at the same time. I am sitting in my office working away and then all the sudden, my mouse starts moving around randomly. I quickly go up to the Bluetooth menu, and I see there is an Arc Touch Mouse paired with my computer! It is bold in the menu. I quickly hit Disconnect on the device and it goes away. Then a few minutes later, it shows up again and they take control of my mouse. I opened up the Bluetooth preferences, and I see the device there too. I removed it from there. Then a few min later, it happens again! I finally turned off bluetooth. Then in the bluetooth preferences, I see 4 Arc Touch Mice that are paired with my computer. I can't remove them without turning bluetooth. So I waited a bit and turned it back and removed them. It's been ok since then for a while now, but HOW IS SOMEONE ABLE TO PAIR THEIR MOUSE WITH MY COMPUTER? This seems like a HUGE security issue. What else can someone attach to my computer via bluetooth with no interaction from me? Please help!

I'm running 10.10.3 on a MacBook Pro (Retina, Mid 2012). And I use a Magic Trackpad, so I can't just leave bluetooth turned off...

Andrew