To say Kobe was not loyal is downright wrong. I don't know if there has been a player more loyal to an owner than Kobe to Jerry Buss. People talk about Phil Jackson molding Bryant but Dr. Buss was Kobe's guardian angel in this league.
When he was 17, Buss is said to have largely impacted the Divac trade for the Kobe draft pick.
Despite Kobe's image issues, rape case, and overwhelming self confidence, Buss was never willing to give up on him.
According to this article by Wojnarowski, at the peak of the trade demand mania, Buss invited Bryant to his home and gave him the option to go to Detroit. The article claims that Bryant was given the dilemma, thought about it shortly, and decided to stay with the Lakers because of his ties to Jerry Buss.
Kobe says in this article Dr. Buss made him realize his faith in him and convinced him to say. Buss preached patience to Kobe and his confidence in his plan never faltered. All of a sudden, the Lakers have the best record in the west, Gasol is swapped for Kwame Brown, and Bynum became a formidable player - a player cherry picked by Buss as well. Kobe came into that season as a different player mentally and the Lakers enjoyed 3 consecutive Finals.
Kobe used his form of leverage to get better teammates, but in the end it was just the words of Buss that convinced Kobe to resign to a team that was the same as the beginning of the off season.