Here's how the model looks in-game:

Here's how the model looks in Blender:

I used Noesis to convert it to MD3 and it looks much the same there as it does in Blender. This only appears to affect HUD models.
I also tested this on a working model from another mod by converting it from MD2 to MD3, and the issue occurred again. Something is happening with Noesis's conversion process or something.
What exactly is happening? It looks like a problem with the normals but I can't tell and inverting them changes nothing.