Hi guys thanks for all your suggestions.
Let's see, here's the assessment:
1. The background object is not transparent-- it's a very large piece of MDL geometry. It's a 24 bit dds texture. I tried switching it to bmp but it didn't change this.
3. There aren't any other transparent objects behind this 'treetop' cube on which the texture is. All the other geometry has transparent = 0 and alpha = 100, and 24 bit textures only.
4. I tried changing the d3d_entsort to all three possible settings. It didn't change anything. This was per the manual's entity:transparent section. It mentions the same problem you describe re: intersecting transparent polygons, but in this case there is only this one polygon. But otherwise I didn't see any other solutions mentioned.
5. I tried using 32 bit DDS, and then 32 bit TGA on the 'treetop cube' to see if this would change things. No difference.
6. I tried adding a block skycube to see if that would help, but no difference.

Each image is of the same stuff, only from different angles. Here the order is from closest to furthest away: treetop, grassy hill thing, purple cube. The purple cube is quite far away.
I appreciate your insight on this!