I have two completely white bitmaps here:
They're there, trust me.
When I put one on top of the other and scale them down with
TextureFilter.Linear I get this:
How do I get rid of the dark pixels?
This is just a guess, but I notice that the edges of your image(s) are anti-aliased. When you scale the images down using Linear filtering, the semi-transparent edges might be set to black, because the filter cannot handle semi-transparent pixels. This is just an idea, but it might be worth a try to remove the semi-transparent pixels which surround the image(s).
The problem was the texture packer that messed up the bitmaps. How I solved it is I premultiplied the bitmaps with white using Photoshop (Export -> Render Video).