Good work Spry, keep it up.
As for your final statement/question, you haven't really misunderstood anything. It is misleading for people to tell others that they don't need to include direct arm work if they want to reach their arm size potential.
True, some people can get away with not hitting biceps directly, but those are the exception to the rule, not the "norm". Either that, or they are arm dominat pullers (meaning that their arm flexors due the majority of work during pulling exercises, and not their back muscles). Those people generally have sub par back development though.
Also, no matter what exercises that you do you aren't going to have 20" arms unless:
a) you have the genetic potential to, sorry but it's the truth
b) put on a significant amount of muscle all over the body
Now, before anyone jumps down my throat for saying that chins won't build biceps, they will. But, doing pulling movements alone (while neglecting direct arm work) isn't going to allow the majority of people to reach their potential arm size.
If sports performance is your primary goal, feel free to neglect direct arm work (or if you've got great arm genetics). But, if bodybuilding/building muscle is your primary goal, then I'd strongly suggest doing some direct arm work.