Several apps (e.g. @GIMP_Official, @Apple Preview) do not actually delete content from images with an alpha channel. They simply create an alpha-channel tunnel through the content you think that you're removing.
You may think you've removed content, but it's just hidden.
pbs.twimg.com/media/EN8zPZeX…
What if you change "format=png" to "format=jpg" ?
pbs.twimg.com/media/EN8zPZeX…
You how get the image, but Twitter removes the alpha channel for you!
1) Open pic with an alpha channel
2) Cut out content
3) Save as PNG
4) Send it to compress-or-die.com/analyze
So perhaps just GIMP for now.
I'm curious if anybody can confirm another misbehaving application.