Sorry if I try to correct/extend this
Also, keep in mind I neither own nor know PSP.
Redband emailled me the DDS and it was indeed shot as he says. He then sent me a TGA and it was shot exactly the same way (either no alpha channel or all of the alpha channel says "100% opaque texel").
So, it does NOT seem to be a DDS export issue, but either an issue with the original picture or with export / save as in general.