You could calculate it by taking the average lifetime of a tree and dividing by the length of time slept and the number of trees in squashing distance.
Only if tree death is uniformly distributed over a tree's lifetime for some bizarre reason. And it isn't.
The logic in the story is BS. First, you would never, ever get into a car with that logic. Second, trees just aren't that ephemeral. People who live in a forest would be very aware of when they do or don't fall (or more problematically, drop large branches.) It's not as straightforward as just avoiding storms or dead-looking trees. Sustained wet weather, especially after a period of dry weather, is a common cause. As is the opposite for some trees (eg oak trees drop limbs in sustained hot dry weather.) As for disease or other causes, an experienced hunter in a familiar area could tell at a glance.
The message I got from the story is that they probably did have a very good reason. They either thought it would be too hard to communicate, or they were themselves cargo-culting the falling tree excuse when the reality was more likely to be... I dunno, snakes or nasty bugs or annoying sticky sap or whatever.
I think your explanation is pretty plausible, I wonder why people are downvoting it.
Like these guys probably have homes, with bedding of some sort, maybe they'd rather sleep next to their wives than some caterpillars. If I was giving somebody from a far-off place a tour of my workplace and, on the bus ride home, they suggested it was getting dark and we should camp on the sidewalk I'd probably not go for it. If they were really insistent I'd probably amplify the danger of sleeping on the sidewalk to shut them up.
> First, you would never, ever get into a car with that logic.
The logic isn't applicable to any set of risks. As deadly as cars are, the risk of car crash death is much, much lower than 1/5000 per trip. It's probably closer to applicable to being a drunk driver, and "you would never operate a car drunk" is pretty accurate for many people.