Engines, I agree with absolutely everything you say apart from your "And that, people, means that they aren't 'safe'" bit.
Airworthiness confirms a level of safety. The lack of airworthiness, in itself, doesn't automatically mean that a system is unsafe. For sure, there is a much increased likelihood and undoubtedly an un-airworthy aircraft is less safe than an airworthy one but it may well still be (acceptably) safe; we just wouldn't have the ability to make such an assertion.