I always see it pointed out, when discussing how to handle/avoid bear encounters, that black bears can climb trees. Granted, but does that matter? Has there ever been a case of a black bear pursuing someone up a tree in order to attack them?
It seems logical to me that bears wouldn't fight in a tree like that unless forced to as they are busy using claws for climbing, but I'm not exactly an expert.
The question asks for an instance where a bear climbing a tree attacks a human. I found a news article of a hunter being attacked by a black bear in a tree.
I don't think this is a completely satisfying answer since the question implies the question: Why would a bear expend the effort to climb up a tree to attack a human? I am not a bear expert but I read this article which states that bears are known to kill one another by throwing each other off the tree they're fighting on. So your assumption that the bears are busy using claws for climbing might not be true. In fact, bears are quite capable climbers as shown in this insanely cute video.
EDIT: I didn't explicitly answer the first part of the OP: Does it matter?
Given the fact that bears are capable climbers, and given that they have inflicted damage while climbing, would lead me to assume that their ability to climb trees does matter when one is trying to avoid being harmed by a bear.
I know that if you cross the Bering Strait to Northern Asia (Siberia, etc.) you'll find that bears hibernate in huge nests in the tops of trees. So climbing trees is not a problem for bears. They must do it in that region because there are tigers about. The real question has to do with the nature of the bear in question. I've turned about in the woods to find a brown bear lumbering by me with his shoulder at the level of mine and behaving as if I had the culinary interest of a rock. To my knowledge only Polar Bears actively hunt humans.
They are faster and can climb better than you, so if they want you they can get you. They rarely see you as real prey so they might not climb a tree to get at you, still... its a risk
In this video you can see a bear climbing a tree where two hunters are. At first it looks like it could be the same bear you saw on the ground, but it's not, it's one bear running away from another, and at the end it climbs another tree to escape, so you can say they do it too. On the other hand I wouldn’t be able to climb as fast as this bear does and I'd be caught on the ground while hugging the tree swearing :( But just look at how fast the whole chasing and climbing is, can you do better?
Chances are any black bear you encounter will be more frightened of you than you are of it, and it is unlikely they will chase you up a tree unless they are provoked. They definitely can climb trees, but they most likely will not chase a human up a tree nor attack unless provoked or protecting their cubs. They're primarily interested in your food.
In this video (which is required viewing for anyone going into the Boundary Waters Canoe Area Wilderness), they discuss how to handle an encounter with a black bear at around minute 8. This should reassure and also inform you what to do if you encounter a black bear.
Brown bears and grizzlies? That's a different story.
A few years ago I was walking in the woods in western Washington state (USA) the forest was Douglas fir, with undergrowth ranging between 2 and 10 feet high (1 - 3 meters). There was no trail.
I was trying to be quite as I was hunting squirrels with a 22 rifle. The area I was in had brush about knee high.
Suddenly a short distance in front of me I heard a lot of noise in tall bushy area. Three black bears came storming out of the brush, running in different directions. I was standing about 2 feet from a tree, and I side stepped to get behind it. All three where different sizes, I don't know but I think it was a mother and two grown cubs of maybe 2 and 3 years old.
One went well away from me and the other two came in my general direction. One bolted between me and a nearby tree. The last was running nearly directly toward the tree I was hiding behind. At the last moment it choose a tree just to one side. It went up that tree at the just about the same speed it was running through brush.
The one in the tree only went about 20 feet up and stopped, I could still hear the other two running through the brush. A few moments, it was quite, my heart was racing and I was scared. I moved away from the area, in a direction that bears did not go, slowly until I had some distance between the area of excitement and myself. At which point, I ran.
The choices I made may or may not have been the right ones, but I gained two sure points of knowledge.
Point 2 is important, because the first two things that went through my mind were; I have a 22, this not a viable weapon for a bear, followed by, I should stand in front of the tree to hide my silhouette, so I can keep a better eye on what is going on. All of this happened FAST, I didn't actually decide to step behind the tree it just happened.
My answer to your question "Will Black Bears actually follow you up a tree?" is 100% yes, they will climb right over the top of you to get as far up a tree as they can so you can't get them. When you and a black bear become aware of each other, do your very best to stay out of his escape route.
