Since being a free paladin doesn't seem to grant you any kind of payment, I would agree that people who become free paladins will, most likely, do so for the sake of helping others. However, you can believe in helping others, join a group that does exactly that and still find yourself taking and justifying evil actions:
Both a Sultarnsworn and a free paladin, no matter how much they dislike politics, could pick a group of brigands and decide that torturing them to find their leader's plan is justificable because of the greater good ("We torture these brigands today but we'll catch their leader or ruin their plan, saving many innocent lives").
If this does or does not make you evil could be discussed, but the point is that we shouldn't think that the Sultansworn are inherently more propense than free paladins to evil or unlawful actions than free paladins because of the politics involved in their organization.
Both a Sultarnsworn and a free paladin, no matter how much they dislike politics, could pick a group of brigands and decide that torturing them to find their leader's plan is justificable because of the greater good ("We torture these brigands today but we'll catch their leader or ruin their plan, saving many innocent lives").
If this does or does not make you evil could be discussed, but the point is that we shouldn't think that the Sultansworn are inherently more propense than free paladins to evil or unlawful actions than free paladins because of the politics involved in their organization.