I work for a software company and I sometimes get the same problem when rendering images in OpenGL
The problem is not Darkbasic, the problems is the settings specified during export...
The image bellow is a PSD formatted image, as you may already know, the checker background represents opacity or transparency value...
When I created the circle on the top left, I had "anti-aliased" turned on... This feature will smooth the jagged edges of an object by softening the color transition between edge pixels and background pixels by using alternative levels of opacity as you can seen from the enlarged section of the circle.
When exporting an image to DarkBasic, make sure that you use a adequate format so that the opacity color information is not lost.
An alternative would be to make sure that anti-aliasing is turned off.
If I export this image as a GIF image, the pixels with 25, 50, and 75% Opacity would turn blue, red or any custom background color specified when exporting. This happens because a GIF image only supports solid pixels or 100% opaque pixels. If my circle was a different color and not black, I could choose a black as my custom background color. But if I did here, my circle would also become transparent. I could re-draw my circle with a lighter shade of black.
A BMP image works the same way, you must choose a color as the transparent color or "mask". If the background color specified was a blue, the anti-aliasing would turn that blue into darker shades of blue... The blue background would show transparent in Darkbasic, but the darker shades of blue would not show transparent. So you get a blue border around the image.
Darkbasic supports PNG images, PNG can hold different levels of opacity. As long as Darkbasic can read the PNG correctly, you should not have any problems because not only the blue is specified as a transparent color, but also it's shades of blue from the resulting anti-aliasing.
To save time and headache, I would simply turn anti-aliasing off when creating transparent backgrounds and if possible, choose the darkest color for the transparency. Also, exporting as a transparent PNG image is probably your best option.