When «Always maintain stock synchronization for re-published products» (global) is chosen, it’s not possible to chose «If checked, any stock change will synchronize across product tree.» (single product).
When «Always maintain stock synchronization for re-published products» (global) is **not **chosen, its possible to chose «If checked, any stock change will synchronize across product tree.» (single product) for any product individually.
Stock sync. has nothing to do with «Child product inherit Parent changes» (single product)». «Child product inherit Parent changes» (single product)» is about product data.
When «Child product inherit Parent changes» (single product)» is chosen, product data will sync. (except if you in the main plugin options have chosen NO to inherit title, description, price or category for each site) If it’s not chosen the product data will not sync and you can change the child products data without it being written over by the parent product when updating the parent product.