Like Sir William, I grew up with the King Arthur style stories (and a lot of Disney, too). One thing I've realized as I've gotten older is that in the 'real world', kind actions to an opponent doesn't always make them a friend; make the effort at peace, but brace yourself at the same time, in case it comes to conflict.
I've also started trying to look at things from a modern perspective, and a medieval perspective too; I posted a link to a story of Sir William Marshal in which he essentially robs a couple who is eloping, in order to prevent them committing usury. With robbery not being chivalrous today, but acceptable in period, it can give a different 'feel' to the story sometimes, and it seems as though some stories may be 'out of context' with a 'modern' perspective.
I think people in general consider chivalry as the typical King Arthur tales, and as they were told during the Victorian era. If we told them it's chivalrous to defend the weak and be generous, they'd likely agree with us. If we told them it's chivalrous to relieve someone of their possessions if it prevents them from making poor choices, it would probably be difficult to convince them otherwise.