“…I thought that as an Adobe product, a *psd file would be handled correctly. “

 Well it does…I was just giving a quick and easy answer that works (KISS= Keep it simple SWAMP, or you’ll confuse the crap out of people).
A Psd file with transparency works fine as long as it is not a background layer (layer from background..) or you haven’t merged it with the background, or you delete the background under the current layer, or…..( fades out into endless babbling).

 The difference is both GIF and PNG have kind of a “built in” alpha/trans channel/mask (whatever), where a Psd doesn’t.

 

SWAMP