There has been some debate as to the kinds of fights the Gracies were challenging other top level fighters to and that includes their fighting events such as the UFC. As some people have pointed out, the UFC and the rules that the Gracies were proposing for their fights were not rules that favored the Gracie system, they were just rules that allowed just about every and any fighting system. I would have to agree that the rules did not favor the Gracie system but I will say this. The Gracies trained to fight in matches where both striking and grappling was allowed. Some, I would say perhaps many of the fighters they challenged were top level kickboxers and people who trained to fight in matches where only striking was allowed. Therefore they did not train to fight in matches that allowed both striking and grappling like the Gracies did and so that is why they turned down the challenges, they knew they would lose against the Gracies because they didn't train to fight in matches where their opponent was allowed to tie them up and neutralize their striking ability. On the other hand, the Gracies did not train to fight in matches where that wasn't allowed and so they would no doubt lose if they fought under those rules. So while the rules that the Gracies were proposing didn't particularly favor their style, they were rules that the Gracies were at least used to fighting under.