Don't get me wrong, I'm not trying to be beligerant. We value experienced advice in here. The point of these forums is to help new homeowners figure out what's causing the problems they're having. But, when apparantly knowledgeable people all propose different reasons, about the only way the newbie has of determining which ones are plausible are by running them all through a "reality filter". That is, to carefully consider each alternative explanation for the problem and see whether or not it jives with the reality of the situation or not.
Specifically, I think the two statements you made that wouldn't pass through the reality filter are:
A) checking to see if there's mold between the paint and the sheetrock paper, and between the paper and the gypsum, because of the possibility that the white stuff came through the wall, and
B) not being able to kill mold.
If the original poster can clean that white discolouration off the blue paint so that there's no visible evidence of it anymore, and the previously affected area now looks just like the unaffected areas, wouldn't that prove that the white discolouration was deposited on the paint from outside rather than having come through the drywall, primer and paint to accumulate on the surface of the wall? That is, if the mold is white, and it passed through a layer of clear plastic with blue pigments inside it (the paint), wouldn't there still be some white "mold" particles still in that clear plastic film that would give it a whitish discoloration? That is, the white "molds" still in the paint film would act the same as white pigments to effectively whiten the colour of the blue paint, making it a "light blue" colour instead. If cleaning the paint film with bleach were to make those white "molds" clear, then wouldn't that bleach also affect the colour of the blue pigments inside the paint film, too? So, wouldn't the apparant lack of any discolouration of the paint film after cleaning prove that the mold didn't come through the paint film?
And, about killing mold...
When I clean a dirty wall with bleach, I get dirt accumulating on the damp rag or sponge I'm using, and the cleaning water I use gradually gets dirty. However, when I clean mildew off of a painted bathroom wall or ceiling, I don't see the sponge or rag turning dark, or any substantial change in colour of the bleach solution I'm using. If it's not possible to kill mold, then what I appear to be doing is only changing it's colour from black to clear. It seems to me that if I didn't kill the mold, I would soon see mold growing on the wet rag or sponge I used to do the cleaning with. I've cleaned mildew off many bathroom walls, and have never subsequently seen heavy mildew growth on the cleaning rag or sponge used to do the cleaning. In fact, I believe that if I used a cotton rag to do the cleaning, rinsed it out and put it in a plastic bag so that it wouldn't dry, mold wouldn't grow on it any sooner than a clean wet cotton rag under the same conditions. So, if the bleach on the rag didn't kill the mildew and it's spores, why doesn't the wet cotton cleaning rag become a growth media for mildew?