TL;DR: There are lots of positive diplomacy modifiers, some passive, some active. These are more than enough to offset negatives.
Different games seem to lead to different results. I think a great deal of it is the AI Civs involved, and has been mentioned, the player actions. I think more experience with G&K will show us whether the AI diplomacy behavior is fairly consistent or variable.
In my current Emperor / Epic / Large Islands game as England, I spawned on a continent with Ethiopia and the Huns. Ethiopia was fairly close to me, the Huns were far away. Of course, the Huns tried an early rush, which I beat back. They would not sue for peace for a long, long time. I eventually settled a city between us, and then took 3 of their cities, leaving their capital alone. They were ready for peace once I started taking their cities. Since then, they have been super friendly, minus the odd incident of tech stealing (I can't blame them, they are way behind now), and they were apologetic about it. Been nice trading partners too, buying up some resources from me for some handy GPT.
Ethiopia, despite spreading Christinity to me, launched an attack, probably because of our close borders. I easily pushed it back and they immediatly sued for peace. Since then, they have been very friendly.
The rest of the world has been amazingly friendly to me. Every other world power has been friendly to me. Greece was friendly, but has become fairly hostile due to my friendship with their enemy, America.
Here is why things have ended up this way:
1) I didn't found a religion and haven't pushed it on anyone. I was beaten out on religions, but received Ethiopia's fairly early, and it has proven useful to me. This has helped me maintain relations with Ethiopia despite our close borders (the one border war aside), and helped me maintain relations with the rest of the world because I haven't been trying to convert them.
2) I didn't finish off Attila. He attacked me, and would not sue for peace for hundreds of years until I captured his cities. I don't know if I would have gotten a warmonger penalty for eliminating him, but I think that would have been likely. I would love to see a confirmation of what exactly causes a warmonger penalty, since it seems to varry so much.
3) I have stayed on my continent. There is room to expand, and I am starting to plan some colonies, but until now I have had zero border conflicts with anyone else.
4) I haven't competed for City States.
5) I am #2 in score. Right now Byzantium is #1 in score. Not sure how the AI views score now, but I suspect that not being on top helps.
6) I have maintained a reasonably sized military.
7) I have traded as often as possible, with as many other Civs as possible.
8) I have accepted DOF from lots of people. This has led to multiple 'friend of friends' bonuses, and only one negative (Greece, as mentioned earlier).