So if the staining is from splash marks (before there were gutters) why are there similiar markings on the gable end of the building?
I agree with Mike. I have seen this many times. Thermal imaging, within 3 - 4 days of a pretty good rain, has often confirmed it. Note the blue arrow that Mike added to the picture and extend it down (and curved in towards the house). The stain marks are right in that path. I bet if you ran a hose up there, especially if there was some wind, that the over flow water would splash right onto those stains.
Remember, brick is a sponge. It absorbs water and all you need is some cellulose material and you have mold from New Jersey.
Moisture readings on the inside wall, right at those stains, would be excessive.
Sure, put on a cricket, kick out flashing for the gutter and maybe wider gutters, but I would say that the damage is done and inside the wall. It would call for some pretty heavy remediation.
At least, that’s my take.
Recent install of a vapor barrier and the splashing around the bottom perimeter indicates the sellers should have knowledge of a moisture issue that should have been disclosed.
The dark staining may be an algae rather than a fungus similar to Gloeocapsa magma which loves lime stone (an ingredient of mortar used in the masonry) and more commonly found on composition roofs. The staining is a result of an accumulation of the algae dead, dark colored cells.
Just my S.W.A.G. 
Some of the staining could be from when it was built mud splash really soaks into brick and stucco. Someone might have been to lazy to was it with muratic acid! And or put straw or hay down during construction.
The lack of kickouts was the biggest problem.
I think there are two different processes operating here: overshoot at the gutter ends adjacent to the chimney (or previously missing gutters at these locations), and splashback (and/or rising damp) at grade.