I think one or two people are missing the point I was trying to make.
While it clearly true that trees will stop the flight of many shots, so preventing them reaching and possibly hitting other people on the course, they will not stop ALL errant shots. Balls fly over trees, around trees, and even straight through trees.
More importantly however, trees - especially in full foliage - obscure vision. In the example I used at the start of this thread I genuinely thought I was the only person within a quarter of a mile, so when I saw my ball flying over a stand of trees towards the next tee I did not shout a warning. As a consequence someone very nearly got hit.
If the trees had not been there, I would have seen our greenkeeper on the tee and given a lusty shout of "FORE!!!". He, at the very least, would have been able to crouch down with his arms over his head to minimise the chances of being hit and injured. He would also in all probability anyway have been aware of my presence and seen me taking my shot. In this case he would have had a good chance of following the flight of the ball in the air as it flew towards him.
No-one is suggesting that upon hearing a shout of "FORE!" golfers can pick out an incoming ball in the sky. That's not how it works. Sensible golfers, upon hearing the shout, will cower down or seek immediate shelter behind their bag, cart, or whatever. The problem with "protective" trees is that even if the shout goes out, confusion reigns for that vital couple of seconds as people look around for where the shout might be coming from.
Most golf courses, particularly those on tight plots of land, have instances where holes run parallel to each other in opposite directions. In my experience, if there is a good view of gofers playing the adjacent hole a natural protocol develops whereby players take their shots in turn, and so are aware of errant shots coming their way. If someone hits a ball towards other players he will invariably shout "FORE!", even if he thinks that they already know that his ball is heading towards them. It is simple good manners and etiquette.
Trees can change all that.
Trees give a false sense of seclusion, of separation from the rest of the golf course. Unless one specifically knows that one's misdirected shot is headed towards other players, the first thought that enters one's head tends to be "Shit! - I'm in the trees!" The thought that your ball might fly the trees and endanger unseen players beyond comes a second or so later, and very possibly a second or so too late.
About the only instance I can think of in which trees can be essential in promoting safety is where significant movements in the land make players on one fairway invisible from the adjacent one. In this situation a barrier of trees might well be the only way it is possible to afford protection to players on either hole.
In general though, my question in the title of this thread was rhetorical. I firmly believe that safety is enhanced on the course when players on adjacent holes can see each other clearly. Safety is compromised when players are unaware of the presence of others due to a screen of trees.