Uncontrollable variation in BG color of transparent Background Image

[sethcshort]

I'm working with Background Images that have transparency.

I'm finding that PNGs created with Photoshop have a white background, but PNGs created with Illustrator have a black background.

And sometimes if I edit an Illustrator PNG in Photoshop and then save it, it has black framing the opaque areas, and white elsewhere. This is visible in my third attached image, both the black and white in the non-opaque area are transparent.

Is there a way to control the background color behind transparent Background Images? It seems to operate independent of the Color environment setting.

Attached are cropped screenshots, and the original background PNGs I used in case that helps.

Thanks,
Seth