It depends on the "color" of the fully transparent pixels. If they are black (RGBA 0, 0, 0, 0), a black border is going to appear at blurring or resizing. You won't see this effect so heavily if the transparent pixels have a white color (RGBA 255, 255, 255, 0), but it is certainly ugly with mixed colors of transparent pixels (like RGBA 255, 0, 0, 0).
Here are some reference images explaining what I mean

In the first column you see the original image. In the second column you see the background pixels made visible. Notice that the shadow around Pac-Mans feet is totally black. When blurring, you can slightly see a black border coming up around his shoes.
This effect can be seen clearly after making the transparent pixels red. If I start blurring the image, a red border appears around the whole image.
In the first image of last row, you can see that blurring doesn't make borders really blurry, only the "inner content".
The second image there is a blurring how I would expect it, done with Inkscape.
The third image shows a scaled down version of Pac-Man, left made with PFS, right with inkscape. Zoom in and you can see opaque black pixels at the bottom right outline of the character (mostly near the shoes) in photofiltre, those are a result of background pixels which became opaque after decreasing the image size.
