This is a touchy subject. Unlike fighting mobs (where the first person to engage the mob gets exclusivity until they either kill it, get killed, or call for help), logging offers no protections/exclusivity. The other problem is, unlike mobs, there is only ONE logging point in a forest area. When a log is harvested, it'll re-appear somewhere else.
I've noticed some very odd things... I watched the logging point go from one tree, to an adjacent tree, to yet another adjacent tree, while one individual expected to claim exclusivity on them because he was able to get to all of them first. The randomness just isn't very random, and though people were, for a time anyway, not using anybody else's logging point, they weren't exactly taking turns with the logging points either.
A second problem (mild) was when I noticed one individual who would spot the logging point, run up to it, and then do NOTHING. They'd just stand there and not atttempt to log. I thought perhaps maybe they just needed to re-sort their inventory to make sure they had an open slot to receive the next log, except they did this several times. It's somewhat rude to others who are being polite by not encroaching on the logging point because nobody else can log (no other logging point will appear until that one is harvested). Maybe they were just new and didn't realize they were supposed to use a hatchet on it.
The last straw was the night that several individuals kept taking my logging points even when I was the first to arrive -- and this was common.
In frustration, I decided that: (a) the authors (Square Enix) obviously KNOW how to grant exclusivity when they want to because they do it with mobs, but (b) they don't seem to grant exclusivity in logging, and (c) logging isn't structured to where you can just go find another logging point... there wont be one. Apparently it was supposed to be a competitive event.
I've thus rationalized that if a person takes there swing and gets nothing, they shouldn't be upset if someone else wants to try a swing to see if they can't harvest a log... after all, there'll be a new logging point available as soon as the current one is harvested and everyone can keep logging. My guess is that if 2 or 3 loggers just went to the same logging points and took their swings, the sum total of logs harvested by the end of the night for each might likely be greater than they could get by trying to have any kind of exclusivity deal.
I now tend to play it by ear. If I notice that the pack of people logging are being nice about it, I'm all for that. But if people are aren't, I'm not going to get upset, I'll just accept it, deal with it, and log that way.