Hm, I'm not sure what your problem is. If you're saying that this occurs in the workspace, it's probably that you're getting weird results because of your graphics card. Anim8or isn't a game engine so it probably relies on the graphics card to automatically manage the depth and transparency work. Mine is an ATI Radeon HD 6970 and none of the transparent textures block what's behind them. Because there is some
Z-fighting on the wings, it could cause different graphics cards to handle it differently, or else just be poor management of the Z-depth due to some overlapping polygons, or else a default setting in the card that doesn't render layered transparency objects well..
Because this is just an opengl workspace issue, it doesn't show up when you actually render it. Go to Render->Render Image... and render what you've got in your workspace, and you'll see what I mean. If you're going to use it only within Anim8or, then you have nothing to worry about. Also, the original model will work properly in any decent game engine regardless of what you see in Anim8or's workspace.
So to summarize: nothing's wrong