The problem - the paint wasn't perfect (both in application and in design). At Mach 3, the paint would peel. This is part of why the SR-71 (being developed at the time) got the special titanium-infused paint that could expand and contract with the heat It's black somewhat for cooling, but mainly for camouflage. Kelly Johnson would have painted it white had there not been concerns about ensuring that it was as stealthy as possible in ALL aspects, both radar and visual (the black paint is semi-Radar absorbing and hard to pick up visually). A white paint was later created for the X-15 that worked, but by then the XB-70 was restricted to Mach 2.5 for other reasons, so there was no further development done. I don't know if Concorde's white paint was similar to this paint, but as was mentioned, the problem with speed is that any "bump" in the paint at Mach 2.0+ will be found and the paint will be peeled. This means that you can't do layered paint jobs. You actually have to have the entire surface level and the application must be completely uniform. Thus why the wash and wax after each day of operations for Concorde.
CT can probably verfiy it but the programe for the XB70 was to paint it with the same black paint as the SR71 - the white scheme was the old Anti radiation flash idea I believe....and I agree with Ben - its a beautiful looking beastie -- and it tied Mig up for a LONG time while they developed the Mig25 to counter it....makes you wonder if some programs were not done just to make the oppostion react..
The book I have mentions black paint as a potential "in service" paint, however I think most believed it would end up white or natural metal. The USAF has never liked "dark" airplanes, especially their "showcase" aircraft like the B-70 would have been.