tl;dr: Experience makes dangerously careless. Examples: quadcopters, lasercutters.
I had a similar scenario with the same preconditions. In this case, one of the propellers came off and barely missed a face.
This was a 10 inch hard plastic prop with some sharp edges. It could've taken an eye out. It could've caused serious cuts. It could've been a carbon fiber prop and caused _serious_ cuts. Of course it could also have been a soft plastic, round edged prop that would've done less damage. It missed, and nothing happened.
In this case, the cap on the mount wasn't tight enough - complete negligence; preventable. But what bothers me it that it is not possible to completely prevent that kind of mistake. Mount caps _can_ shake loose under vibration - with some features (spin reversal) there is no one safe screw direction. Also, mounts can break. More importantly, prop blades can break. Some prop mounts only use rubber loops to secure the props - they props are _meant_ to fly off off in that case. A prop could be inverted, or the PID controller could diverge, potentially sending the entire copter into your face. Probably everyone should wear safety goggles. But nobody does, and things rarely go wrong. At the very least, please do not have your head on _or above!_ the propeller's plane. Search Youtube for "quadcopter hand launch" for an appreciation how often this rule is broken as a matter of normal, routine operating practice. Often the person holding is not the pilot. That's some trust, when a small inadvertent finger movement on the pitch axis could permanently injure.
What also bothers me is that the people who should and do know best often ignore safety the most. Ever seen a group of copter devs scramble as the noise of the copter thirty feet overhead cuts off? Ever seen the same group charge a few dozen lithium polymer batteries that have survived more than a few crashes, unattended, with no fireproof bags, with no fire extinguisher, in someones room? Nothing ever went seriously wrong. But everything could have. And dont get me wrong - these are smart, safety minded people.
Along the same lines, if you are ever near someones DIY lasercutter, say in a hackerspace/makerspace... do _not_ assume it is eye safe, no matter what they claim and what laser safety certs they claim to have. In particular, do _not_ ever assume it is eye safe when you look at it from an unusual angle, like when you bend down, kneel, or when small people, children or pets are present. I have seen multiple DIY lasers get the top cover right (easy - any thick plastic sheet will block stray light from a CO2 laser), and completely and utterly fail to close small holes in front (air vents, or lid not closing perfectly, ...). There's a back of the envelope calculation that looking at the diffuse (not even reflected) spot (invisible! - and there might not be secondary light) a 100W CO2 laser (a typical size for ambitious hobbyists) creates on a surface can cause permanent eye damage if viewed from 1 meter away.