It looked like the texture in the MD2 folder because it is the texture from that folder, but fitted to the SRB2 pallette, and with the primary color changed to green to allow for color changes. When SRB2 does not find a PNG texture for a model in the MD2 folder, it instead uses the sprite that the model replaces as the texture.
In short(except not), remove the textures for any models that are supposed to be affected by this wad from your MD2 folder when you intend to use the wad. Alternatively, you could copy your MD2 folder, remove the textures mentioned from the copy, and just rename the two to switch between PNG textures, and WAD textures. Remember, only remove the PNGs for models that have their texture replaced in the model asset wad you use(which would be md2color.wad).
But first, make sure that it actually is the same texture in the wad as in your folder; if it is not, the wad may be intended for a different player model than what you are using.