The engine manufacturers and aircraft manufacturers create the training requirements, maintenance requirements and certification. It is the airlines responsibility to implement the maintenance per manufacturer instructions. The FAA oversees to ensure airlines have a maintenance management program and that all maintenance is performed per manufacturer guidelines.
There is frequent feedback between airlines and manufacturers. Manufacturers issue service bulletins and provide root cause feedback to airlines. Airlines in turn will let manufacturers know if processes could be improved and request deviations to instructions if necessary. The component-level feed back is direct, that is the engine shop at United would be talking directly to P&W or GE without necessarily going through Boeing, so as to ensure accuracy of information and speed of communication.
If an airline chooses to try to cut corners that will come out (quickly) in the NTSB investigation. But it is the airlines responsibility to ensure maintenance is performed to standard.