Overhead costs are not the same. R&D and management is also done in China lowering the costs.
Furthermore they introduce competition in form of a very low-margin business model:
Currently we have the premium phone lines e.g. maxium size iphones and the budget phones, minimum IPhones (8GB), slow processor phones. Chinese producers can’t compete against the premium models brands without underbidding the price, but they beat out bad component hardware by a big margin with the cheaper brands (Xiaomi, Honor = the budget brand from Huawei). Now the big players can either lower their margin for the top phones, add SD cards etc. or make their budget phone lines better — which will cannibalize their own market.