It is a common mistaken belief that it does. Note that Right to Rule has no impact on whether or not other factions declare war on you in Warband. It is advised that before you start a nation of your own, you prepare yourself enough so that the lords respect/know you.
Remember that you, the player, are just a foreigner in Calradia, and getting right to rule is very difficult. This can take the form of the lords stating that 'You are a lord with no master' and vice versa after you talk to them. Having low right to rule also means that the lords in different factions will not respect you as much when you talk to them. If you have a low right to rule, other kingdoms will take you as a renegade, and other lords may not join your faction when you attempt to persuade them. The higher your right to rule is, the more likely lords will be to see you as the real king and even join you.
This is used when you are founding your own kingdom, and it only appears in Warband.
Right to rule is the amount of respect points you have.
