Like.... what the heck is this?
I got the same darn thing happening.
I have two of the original models from the car template in my new simulation and
one works propely and the other is ******I-up like yours.

The one working ok is the fern model, lp_farn.mdl.
The bad one, doing as your problem, is the grass model...
I haven't figured it out yet, but I expect it's the same problem you've run into.
My best guess is that we both got something hosed-up with the code.

I do run my game with the code "d3d_autotransparency" set at 1, and I still got the same problem with a few models.
When I figure this out, I'll let you know. If you beat me to it, please let me know.