Note that PSP can open a 32-bit image, but will save it as a 24-bit image.
In the case of DXT1/DXT3 and other flightsim textures, a converter such as Martin Wright's DXTBMP converts the image to a PSP readable bitmap (24-bit), and the resulting image gets sent back to DXTBMP where the program saves it in the appropriate format.
Similarly, FS Painter from Abacus, does the same thing... it transfers basically a "screen capture" of the texture into PSP, and gets it back into the correct format when PSP releases it.
This isn't true for PSP7. It opens files in the format it's in and saves in the same format, unless you change it in the colour menue. FS2002 and 2004 use many differant formats, but the files must be saved in the same format as the origionals.