(I do also like the lottery version and use them basically interchangeably, though the shorthand is always "bus factor" for me)
For them, hearing "bus factor" may make it through the barrier and result in an involuntary creation of imagery in their head of someone getting gruesomely hit by a bus, and then the corresponding emotions they would feel (or simply just the emotions, without the imagery).
It's not about having enough people to do the work even if someone quits, it's about having enough people that know how to do something that we aren't losing chunks of knowledge if someone quits (or dies, or gets fired, or gets sick, or etc).
It doesn't make sense to me to treat people as part of a conduit bus that are interchangeable as long as there are enough people.