Hello

I just arrived at the kore, sore, are-section of Season 2
http://www.textfugu.com/season-2/this-that-that-over-there/8-5/#top

The text says

これ: This – refers to something the speaker has in his/her possession.
それ: That – refers to something that the person the speaker is talking to has in their possession.
あれ: That over there – refers to something that neither the speaker or the person being spoken to has. i.e. it’s away from both of them.

My book I’m learning with says, the this and that are referring to things either closer to the person who speaks (kore) or the person who is listening (sore). The that over there part, maybe not even visible (are).
The あれ I understand.
But I’m kind of confused about the これ and the それ part.
Does the something has to be in the possession of one person?
Or is closer by either the speaker or the listener enough to choose between これ or それ?

I do understand the pencil part which is explained earlier in this season.
But what about a newspaper lying on a regular sized table at which two persons are having lunch?
The newspaper is the property of the restaurant owner. One of the two person picket it out of the newspaper holder.
How would you refer to this newspaper: Depending on who touched it last or who sits closer to it?

Thanks