Factory Reset doesn't erase everything?

I erased my iPhone 5 and then restored it to factory settings. I wanted to make sure it was fully erased and reset and disconnected from my iCloud account. But the weirdest thing happened, when I started setting it up of course the first thing it asked for was language and wifi connection. When I tapped my wifi network, it connected to it without even asking for a password. How could this have possibly happened after a factory reset. Shouldn't the phone have completely forgotten the wifi network?

 

Yeah, not sure how that happened. I restored it a second time and still had this issue. Somehow the router and wifi chip in the iPhone continue to remember each other even after a factory software reset.

 

I already sold the phone last month, I wish I had taken a screen shot at the time. It not only connected to my network after being restored to factory settings, the little lock icon that is normally next to the name of the network was oddly located somewhere at the edge of the screen, practically off screen and far from where its supposed to be. It was obviously a glitch in the software and all the surrounding networks had their locks in the spot where they're supposed to be.