I was wrong again.
It's either the TGA, or WED/MED.
That previous statement I made about the sprites of the TGA showing up okay in WED was wrong. Upon closer examination at different angles, they were messed up too:
You can clearly see the back image showing through the front image.
I tried this both with and without the wiki's vegetation script. And that texture is a 32-bit non-RLE tga.
So I don't believe it's my model, after all. And from what I can tell, the tga itself is okay. I even used Grimber's before, with the same problem resulting.
So, the only thing I am left with is that it is WED/MED, namely, the "preview" window as opposed to the actual loaded level. Is it possible that tga sorting does not show up correctly in preview mode, but will in "load level" mode? Could someone else test this to see if it works? I would, but my level script file does not load my level properly yet; truth be told, my level has a lot of models and entities and architecture, and I wasn't planning on tackling scripts yet until this tree tga problem came up, so I am unable to see if the sorting issue exists or not in full level load mode without a working level script.
Thanks in advance to anyone who can confirm or deny my theory with testing.