Info derived from the LV Champions forum from users thoric and intaris
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The transparency of icons is determined from the four corners only. So, if the four corner pixels are non-white, it doesn't matter what else is white, it won't be transparent.
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If there is any “non-white” border which fully encloses an area of the icon, that area will NOT be transparent, irrespective of the colors within.
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Poke a hole in that wall with a single “white” pixel and suddenly the adjacent white becomes transparent also.