Router And Network Question. Using Neighbors ?

Hello,

What a great Forum and asset.

Have something going on that I can't understand.

About a year ago, I had a LinkSys Router hooked up.
The Comcast cable box went to the Router, and then was hard wired to PC.
Of course, it also put out a wireless signal.

A few months ago, I removed it.
Now have only the Comcast box wired to the PC.

My son brought over a new Kindle which he just got for a present.
Amazingly, it connects to, it says, a LinkSys network.
Works perfectly.
But, again, we don't have any Router.

All I can think of is that it is using a neighbors, who never bothered to put a Password or any security on their Router..

Is there any other possibility that I am missing ?

What kind of range do these Routers have these days ?
Our nearest neighbor(s) are perhaps 250 or so away.

Thoughts on ?

Thanks,
Bob