There’s a real dearth of info around coconut fatalities. This 1984 paper examined a 4 year timespan of all trauma-related admissions to one hospital in Papua New Guinea. 9 of them (2.5% overall) stemmed from coconuts. In 3 of the cases, all children, the patients slipped into coma.
From what I’ve read elsewhere (no good links, sorry), coconut injuries worldwide seem to have fallen significantly due to better harvesting practice - the age of a coconut and their chance of falling appear to be linked. While I can’t find a good paper saying this, I do buy it.
So, perhaps not 1:5000, but (at least at one point in time) definitely a risk.
Is it possible that both the original teller, the reteller and you too, are starting from the (unfounded) assumption that the hunters know what they're talking about, and are adapting the facts to fit this assumption?
There could be another reason why sleeping in the forest was dangerous – e.g., poisonous snakes or dangerous animals etc. Also if the temperature drops at night and they didn't have enough clothing, they could get hypothermia and so on.
If the chance was actually 1:5000, the longevity of trees would be similar to that of hunters sleeping under them - or lower, since hunters can sometimes avoid the hazard, but trees are exposed to it every night (and all day as well). Actual data on tree mortality seems to indicate that the chances are much lower than this. Almost certainly they do not make sleeping under trees a significant risky activity.