This is correct, though I can certainly see how someone would come to the conclusion that starting colors are not identical, as default painting mode is less than full opacity, so the mixed color is generally a lot more saturated than plain sRGB.

And a clarification, I wouldn't call this RGB linear mixing, to me that's mixing in a physical light intensity space. Rather, it's alpha compositing in an sRGB color space, which is probably the most common mode. It's possible to verify this by setting transparency to exactly 50%, painting 50% black over white, and 50% white over solid black, verifying that the color is the same, and measuring that - it's very close to sRGB (128, 128, 128). Linear mixing would give approximately (188, 188, 188). Incidentally, this also shows that Mixbox doesn't retain neutral hue when mixing black and white - it gives something closer to (129, 127, 130), a slight reddish-purplish tone compared with neutral gray.