Ok, toying around with Jungles, since they seem to be the easiest of terrains which act "properly"
Jungle01_01.nif - Contains a small square with some trees on it. All of them are located in one quadrant of the vertices when I open it with NIFScope. Pointing the camera to look with Green Arrow pointing up and Red Arrow pointing right, this places them in the NorthWest Corner, which coresponds to the <Connections> field for the NIF in the Art Define.
Trimming all the other FeatureArtPieces from Jungle and loading the game, placing a single square of Jungle results in 4 "jungle chunks", one in the square I clicked on and the tiles to the North, West & Northwest. Passing a road through one of these causes some trees to move/clear.
Not too surprisingly, with Jungle02_02 I open it in NIFScope and see it is in the NorthEast quadrant (again, green up, red right), just like the Connection would indicate.
I trim the XML to only contain this NIF and place it in the world to see the results: Sure enough, 4 "chunks" are placed, North, East, and Northeast tiles and the one I clicked on. Each reacts to roads.
Now, models are NOT my thing, so this is mildly foreign territory. However, the NIF doesn't seem to hold much data. I know that KFMs need to be in the same files as the NIFs they work with, and I don't see how they would use an animation to do the clipping, so that I don't have to worry about.
One thing I have noticed is that if I view the Block List there is an entry for the Shadow and one for the Scene Root. In each of them there is a cute little Painter's Pallet and a trees.dds entry. I can delete either of these without much notable change in the displayed model (deleting the pallet causes things to move from glaring white to a relaxing grey). Deleted the DDS entry and loaded the game, no noticeable difference sadly.
Removed the Pallet, this time the game crashes when loading the map.
Just spotted a ton more information when I had the BlockDetails field set to display as well. Not quite as simple of a file as I was initially thinking from the other view... so I'm heading to bed for the moment

I was really hoping when I opened the NIF that it wouldn't all be one big chunk of trees, but rather a collection of individual ones, corresponding to the ones which can be removed for a road/river....
EDIT: I didn't look at the same NIF you did, but I suspect the boundary boxes you are talking about are the shadows. We're both out of our normal field though

Need someone with 3DS Max to pop in at this stage
EDIT2: Morning update. I mixed some NIFs to see how the connection things work precisely. I placed Ancient Forests (basically recolored normal ones) in the NE, NW, NE NW, NE SW, SW blocks and the snowy forests in the other blocks. Placing the new mesh forest into the game with a single tile gets you mostly Ancient Forest, with a small patch of Snowy forests in the North Eastern corner. But placing a large section of them results in a huge area of Snowy Forests that has a BORDER along the West and South which are Ancient Forests.
The fact it is along the West and South seems to indicate that the NIF used is selected based on which neighbor tile shares the feature. So it would seem that the base tile (no neighbors) is a light mixture of the 15 NIFs. If the neighbor to the NorthEast (and only that one) is also a Meshset, then it uses the NE connection NIF on this tile, and the SW Connection NIF on the other one (combined with the light amalgamation from the base tile).
This is supported nicely by the Mesh in tests by showing Ancient Forests in all 3 tiles when I do the SW & NE tiles (there is still a small snowy tree in the northeastern corner of each tile), and then showing mostly Snowy trees when I instead do the SE & NW tiles (with a cross-hatch of Ancient Forest running from SW to NE on each individual tile)
Now, while an isolated clump is mostly Ancient Forest, a Surrounded clump is ENTIRELY Snowy pine. Not quite sure what to make of that yet. But I am trying to think of how I can use a combination of Jungle, Snowy Pine, Evergreen & Ancient Forest (too hard to tell the difference between Evergreen & standard Leafy to use that one) to see how the meshing works a little bit better.
Also just realized that the trees sway in the wind, so there might be a KFM for them afterall. Perhaps something can be learned from which clumps sway as one piece?
I decided to go simple and just placed one of each of the various types into a blended Feature type, as the NE, NW, SE, SW connection types, leaving the other options blank.
Placing a single tile of this results in all trees staying ON the tile. I assigned Snowy a connection of SW, and it appears on the NE of the tile. So that is how the base tile is made, fairly easy and nice there.
Adding a single neighbor in any direction results in some trees being placed off-tile. In each case it is the Jungle style of trees, which happen to be listed first in the XML. And in each case the trees are sticking out to the North & East if possible (so if I place them to the NorthEast or SouthWest of the base clump, nothing. Place them due West of the clump, to the north, place them north of the clump, east). Jungle happens to be my connection NE. Swapping the order in the XML shows that having Ancient Forest (NW) listed first results in the AF being used each time, and appearing to the North and West of the meshing. So if it cannot find the appropriate connection type it apparently defaults to the first listed in the XML, and since it is placing it in the "wrong" spot, the result is trees appearing on tiles you don't want them to appear on. This becomes much more evident when I place numerous forests on the map, as I wind up with nothing but small clumps of Jungle except at the corners of the forested area where the other 3 begin to show up.