"Save background color" has nothing to do with the image being transparent or not, it just saves the background color data.
In this image "transparent" is your original, and "untitled" is saved with red background color. They are both transparent as you can see.
If I open the one with red background color saved and exported to png, and remove alpha channel the background will turn red.
Attachment:
Transparent-BG-Color.png [ 308.41 KiB | Viewed 3200 times ]
Now fix the edges of the image, because there's some visible white.