I just watched Strange Things Happen At The One Two Point, and just a few thoughts I've got on Riley...
I made a comment on this at the SCS.net forums, but I'll put them here, too.
I don't think she's a refugee from the future. The scene with Jesse and Riley in the change room at the store (it was a change room, right?) has got me thinking that. I think she's just a lost kid Jesse picked up on the way. While Riley did explode at her foster family, saying they'd all be burned and what else, it seemed more along the lines of something she only found out recently. You know when you find out some really bad news and you keep it bottled up inside and then somebody or something pushes you over the line and you just explode? Yeah, it seemed more like that for me.
Furthermore, being a kid trapped in the foster system, I wouldn't be surprised if Riley is fragile and is the kind to latch onto someone the moment they show any sort of affection or liking to her. Again, the change room scene. We know Jesse is a liar, or at least one to 'leave out the facts'. Look at her with Derek- she's clearly got some other motive going on than what she told Derek. Is it possible she wants to stop John from growing closer to Cameron? Yes. Cameron is a machine and the resistance hates the machines (and I'll get back to this later). John Connor, leader of mankind, is not meant to like a machine. Uncle Bob #1 and #2 are exceptions. They were short-term protectors sent back to save him when he was going to be attacked. Cameron is long-term. Anybody is going to at least form some kind of bond with someone who is meant to protect you. If Cameron doesn't become Romantic Interest #1, John will at least see her in a sisterly or motherly sort of way. But I'm going off track.
Going back to resistance hating machines, Riley doesn't seem to be like that. If she was sent back on a mission, she would recognise Cromartie, and she would probably be scared of him or hate him. It's also possible Cromartie would recognise her. This didn't happen when Cromartie came a-knocking when she was home with John. She saw him as a weirdo who barged into the house. Scared? Probably, but I can tell you from first-hand experience, it's not fun when some guy enters your home and starts walking around like he owns the joint. But she didn't seem terrified when she opened the door. She didn't start attacking as Derek or Jesse would probably do. She knew something was up, sure, but she didn't harbour any suspicions of him not being human.
This leads to my theory that when Jesse came back from the future, for whatever reason, she found Riley and realised she could use her to her advantage. Leven posted a note on her website (that I can't find now) that Riley was meant to look sort of 'frumpy' and over the coming episodes she would dress better and become more sure of herself. Riley, while she comes off as sure and perhaps a little cocky, does seem to be uncertain of herself. And Jesse is clearly very manipulative and knows how to fool people. She knows how to drag people into her web. Look at her with Derek in last week's episode. Charlie said love makes people do stupid things. Derek doesn't even truly know if Charlie tortured him. Could it have been an alternate future? Yes, definitely. But Derek doesn't know that for sure.
I wouldn't be surprised if Riley loved Jesse, if only in mother-figure sort of way. I wouldn't be at all surprised if Riley was suffering some sort of Stockholm Syndrome. Look at the way Jesse held her and stroked her hair. The way she spoke to her. She was pulling her further and further in to what she wanted Riley to do.
I think Jesse would have told Riley some of the facts of the future. The nuclear fallout, the war, the amount of people who died. I think she would have told Riley that John Connor was the only one who could stop Judgment Day, or save the world. I think she would have left out the part of robots. You pull a normal, sixteen-year-old off the streets and ask them, what's more possible: nuclear war or robots, they'll probably say nuclear war. This is the world we live in. It's more like that tomorrow a nuclear bomb will drop on my house than a robot will come in and blast my head off. Riley, for all her emotional weakness, is an average kid. Jesse would know that. Riley is also like John in a lot of ways- foster family, not a good background, a little lost, rebels. Riley's also attractive and is looking for a friend. Jesse wants to stop John from attaching to Cameron, so she's probably using Riley as a way to get John's attention (as well as whatever else she's going planned in her mission).
Anyway, those are my thoughts on the Jesse/Riley/John(/Derek) relationship. I don't know how true they are, or what the writers have planned, but if any of it's true, I hope, hope, hope Riley's not from the future. I don't have much luck with my hopes and thoughts on the way shows turn out (but I was right when I said Catherine was a terminator!), but that's my one wish for the way Riley's character goes. I love the twists and turns the writers do with the show- it's like Heroes Lite in that manner, but not in a bad way.