Photoshop :: Layer Masked PNG

I'm wondering how Photo Shop modifies a file that's had a layer mask applied to it, because I'm having a peculiar problem with layer masked images. I ran the following test because I needed to mask an image my sister sent me, & the image was getting messed up when it was scaled on her website:
 
I created 2 PNGs.
 
(1) With one, I created at a black & white image & then replace the white with transparency by applying a layer mask.
(2) For the other, I started with a transparent background & added black. No layer mask.
 
When I open the image which had a layer mask applied (1) in one of the other programs on my computer, the mask is inverted! All the white from the original image shows, & the black is now transparent. That makes me think the layer mask is stored somehow in the PNG file. And it has a different problem when her website scales it - it turns solid gray.
 
I don't have any problems whatsoever with the image that wasn't created with a mask (2).
 
Unfortunately, with the image my sister sent me, I don't have the option to start over with a transparent BG, & don't want to cut out the background because I'm trying not to lose the partially transparent pixels, or leave pixels that have the original background partially showing through.
 
What can I do so that the PNG file created by applying a mask stores what I see, and doesn't need to store the layer mask? I'm using Adobe CS5, version 12.02, on Mac OS X 10.6.