A Balian of Ibelin existed, but he didn't much resemble the movie version.

The real Balian was born in the Levant to an influential family. He was the third son, and so only held minor titles early in his life. He married well, marrying the widow of the former King of Jerusalem and niece of Emperor of Byzantium, Maria Comnena. As such he got intimately involved in Kingdom politics, he was after all now the husband to King Baldwin IV's stepmother. In fact he occupied such a respected position that when Baldwin IV had his nephew Baldwin V crowned Balian was the man who carried the child on his shoulders for the ceremony.

Far from an unknown outsider, Bailian was a court intimate. He also was apparently trusted and liked by both Guy of Lusignan and Raymond III of Tripoli. He also competed with them for honors, and at one point made a play to be the power behind the throne, trying to place his step-daughter on it. So the image of him peacefully farming while Guy and Raymond plotted is inaccurate. He was in the room plotting at times with and at times against both men.

He was at Hattin. And he was the one who surrendered Jerusalem to Saladin, although neither of those scenes went down quite the way they were portrayed. After the fall of Jerusalem he moved to Tripoli where he remained deeply involved in Kingdom politics, eventually placing his step-daughter on the throne... well sort of. They never reclaimed Jerusalem itself, and her husband Henry didn't take the title King, but as much of a throne existed Balian was the power behind the throne. He was also the one who negotiated the peace treaty between Richard and Saladin a few years later. What he certainly didn't do is run to France with his Sibylla to become a blacksmith. As far as we know he was never romantically linked to Sibylla, who was after all his wife's half-sister.