Know anything about Fair Use Guidelines for Photos?

Reach the World is asking for copyright on all media we post to their website on our upcoming journey. It seems kind of silly to me, and I don't understand why they would need that - but they are adamant. In all reality, we are OK with it for the most part. We can always rewrite the educational articles (and probably would anyway) if we decided to publish them somewhere else. However, we are concerned about our photos - we can't retake them.

We have a couple of options here. We could not go with RTW at all, but they seem like a perfect organization for us. Or we could give them crappy photos, but we really don't like that option either. Or we could try to take two photos of most things and give them one and keep the other ourselves. But we aren't sure how different the photos need to be in order to be considered "different". If we take two photos that are similar, but not exact, would we lose the copyright to both photos by putting one on their website? If you have any links to places we could find out exact information, I would really appreciate it!!

For some reason, this organization is adamant about holding copyright of everything posted to their site. I suggested giving them exclusive rights for a while, but that didn't fly.

We'll just give them our throw-away photos (of which we end up with MANY!), or some that are similar. Seems crazy to me, but I guess that's the way we'll have to do it!

Ok, so let's say we are at some historical ruin and take 100 photos. Of course, the ones we think will be GREAT we take over and over again - from every angle possible to be sure we get a good one. There are only slight differences between them, but we decide which one we want to keep and send another to them - it's very similar, but not exact. Does that constitute a different photo? How different does it have to be to be a different photo? Or does it matter? What if we take two photos that we can't even tell the difference between (of course, there will always be subtle changes, but sometimes you can't see them unless you really scrutinize the photo)?