OK, I get the stuff about a folder for your child theme with a style file and I get that you can have a custom functions.php file with nothing but additional functions and wordpress will load both the parent and the child It's those *OTHER* theme files that I'm confused about.
As I understand the codex it says that other child theme files such as templates will be loaded INSTEAD of the parent. So... say the parent has functions A, B, and C, and you want to *MODIFY* function B and add a new function D. That suggests that your child version of this file must have a complete copy of everything in the parent plus your mods? If so, then the advantage of a child is less as when you upgrade you have to check to make sure your mods still make sense. It really should have a device called hooks and I understand that some themes do but I don't think mine does.