The brush is working with the altered image data, and the data is has to work with depends on the how the saturation reduction is performed. More precisely, it depends upon which colour space the desaturation operation is carried out it.
When you work in HSL, you can reduce the magnitude of the S (saturation) component to zero while leaving the angle of the H (hue) component intact. In other words, there will be no colour, but there's a specific colour that's not there for as long as you keep the data in the HSL space.
When you work in RGB, on the other hand, the only way to reduce the saturation to zero is to make the red, green and blue values identical for each pixel. If you then try to figure out what colour is there, well, the data are missing—there is no way to determine a hue angle from the RGB data, so there's no way to increase the saturation of the hue that should be there. And if you convert an adjustment you have done in the HSL space back into the RGB space, you lose the hue angle component as well.
From the behaviour you're describing, the Basics saturation slider works in RGB mode. The name alone will tell you that HSL->Saturation is working in HSL mode. Thus the saturation brush will work with HSL->Saturation to zero, but not with the Basics saturation adjustment to zero.