Inspection intervals are based on expectation of damage over time, not to verify if the installation procedure was properly followed.
Design requirements for airplane parts that experience rotation or are part of control systems are regulated to have locking features to prevent loose bolts from happening. If the initial installation was done improperly it could be a failure in quality control at Boeing. Or if they were installed properly but weren't designed with sufficient locking mechanisms it may be an improper design. Either way this could turn into an Airworthiness Directive which is when the FAA steps in to ensure safety.
This is not true at all. You're right that planes aren't like cars, but airlines absolutely do their own maintenance. The maintenance program is initially provided by Boeing and modified by the airline based on statistical monitoring of issues.