It's because of the watermark they added.
Something like GIF or PNG-8 is great for GBA screenshots because they're 8-bit, so they can preserve the color-limited image perfectly, but once you start trying to add extra colors they just start to maul things. And since PGC's watermark is semi-transparent, it adds a lot of new colors.
What PGC could probably do is make GBA pics in PNG-24, and then run them through a PNG compression program, which should give bitmap perfect image quality in the small area around the watermark, and would still have GIF-like data compression over the rest of the image, without the ugly JPEG artifacts.