NASA's manned flight losses
"NASA's manned flight loses were entirely down to things that were thought to be reliable or impossible turning out not to be so."
You should read the Space Shuttle disaster reports. The only people who thought that the Space Shuttle was super-reliable and couldn't go catastrophically wrong in the ways that it did were some of the management at NASA.
Richard Feynman had one NASA manager tell him that the launch failure rate for the Space Shuttle was predicted to be 1 in 100,000. NASA engineers told him they expected a launch failure rate of closer to 1 in 100.
The engineers knew perfectly well what its vulnerabilities were, and had a pretty good idea what the real flight failure rate was likely to be.
That's not to say that you don't need proper quality control methods to ensure reliability, but it's simply wrong to state that, for example, no-one knew about the problems with the Space Shuttle's solid fuel booster o-ring seals before the Challenger disaster. Even NASA management knew the seals were dodgy, but spun words around the problem in the hope that would make it disappear.
And the idea that only NASA's traditional contractors can be trusted with manned space flight doesn't make sense. Engineering is engineering. If you've got good engineers working under good management, if you make reliability a prime concern, and if everyone does their job properly (including following suitable quality management procedures), you'll end up with good reliability.
It's how come, for example, the Saturn I and the Black Knight rockets managed a perfect reliability record despite their builders not having had a vast amount of experience in the business.
(Okay, okay, so Wernher von Braun bossed the Saturn I project and he did have a lot of experience and yes it used a lot of flight-proven hardware. But still, it was early in the space race and was trying out a new approach.)