From what I can tell from the Technicolor Wiki page (which is very good), the Technicolor three strip process was really just two strips in the camera. The beam splitter formed two channels to illuminate the two strips. One of the strips was a sandwitch of two films with their emulsions facing each other. One of the beamsplitter channels was filtered for the green channel and illuminated one strip and the other illuminated the sandwitch which formed the Red+Blue channels. The Red and Blue sandwitch was latter stripped apart.
*** Enter Conjecture ***
Something tells me that Technicolor films are really more like automatically colorized black and white movies where the luminance information is taken mainly from the Green channel and the color is overlaid from all three channels in the dye transfer process. It would seem to me this would prevent the need to micro-register the luminance information in the two strips (three channels) separately formed by the beam splitter. Otherwise it is hard to believe they could keep the process tolarances tight enough to register all three channels without leading to a fuzzy print.