Hey Erick,
You already read some of my thoughts on Organizing Styles as it relates to style inheritance. There's also a fundamental issue with syncing based on style names and folders.
If your style source document has the folders in it, your destination documents that you're syncing to will also have the folders. Others have pointed out that “syncronization” isn't two-way. Styles will come from whichever document is defined as the sync source.
When you edit one of the other documents (adding styles, sorting into folders), but the edited document isn't defined as the sync source, nothing will change. Changes in other documents won't be global unless you sync from the edited document. This is because you may not need EVERY style in every document. However, be careful if you re-organize your styles into folders AFTER you've already assigned the styles in the documents. You will end up with duplicate styles because InDesign only syncs based on style names and folder names.
So, be very wise when using style folders.
Below are more of my thoughts on syncing styles with Folders…
Importing folders
It might be better to think of “syncronization” between documents in a book more like “Importing.” You're in effect choosing from a range of styles, master pages, color swatches, etc. and having them added to a destination document. If the destination document already has a style of the same name, it will not add a new style, but instead import the incoming style definition.
The sync recognizes styles based on folder name and style name. If the destination document does not have the styles in folders, you will get the folders and enclosed styles added to the destination (and they'll likely be duplicates). If it's not a complex document, you can delete the old styles that aren't in the new folders and re-assign the content to the imported styles (inside folders) when prompted.
Name folders wisely & avoid renaming
When you define your folders for styles, name them well as you will not want to change them after you've “synced” from the source document to the rest of the book. Again, InDesign will think that it's a different folder in the destination document and will create a new folder with the source document styles.
Does this help?