I haven't noticed that the AI opponents have any problem declaring war on each other or me. In the game I have going now, even Ghandi of India is quite agressive (maybe it's something in that vegetarian curry he keeps pushing on me hehe). They make mutual protection pacts, alliances, and embargos galore. Japan is the other big power in this game, but they are actually quite tame. They have let me peacefully grow along the southern coast of their continent after having wiped the Babylonians out. The Japanese leader is actually quite friendly and helpful, asking after a recent deal "Is there any other little thing I can do for you?" hehe.
In my last game, I was the most peaceful country, but everyone else was slugging it out with someone most of the game. After Germany and Russia wiped out England, they occupied one half of the world, with me (Romans), Greece, the Aztecs, Egyptians, and a puny Iriquois nation on the other half. The Greeks and Egyptians were by far the most powerful on our side of the world, the Aztecs were a little ahead of me, and the Iriquois were doing good with what they had, but only had a couple of cities. The Greeks and Egyptians were constantly getting dragged into each other's wars with Germany and Russia through mutual protection deals, and occasionally the Aztecs and Iriquois too. I managed to stay out of the fray most of the game, mainly because I had no iron of my own or rubber, and had to get rubber from Russia, who was always aligned with Germany.
When I was able to trade for iron and rubber, I built up my forces as best I could, then tried two different paths (love that save game feature hehe). The first time through, I invaded the Aztecs since they had iron and rubber not far from my border. Big mistake! Before long, Egyptian modern armor, including an army of it, was pouring into my country, apparently with a scorched earth mandate. Cruise missiles, B-2 bombers, you name it, were raining down on me. The Greeks joined in too. In the second run through, I maintained my "stay out of trouble" attitude, and deployed my forces to defensive positions. Eventually the Aztecs made some silly demand, which I refused, and then they attacked me! When I counter-attacked their territory, Egypt and Greece joined in with the Aztecs to clobber me, with extreme prejudice hehe.