Well, I can’t say that I caught the green when I saw The Matrix in the theater, but when I saw the two sequels in the theater, I very much noticed it. I can’t say that the extent of tint in the blu-ray is accurate, but I would say the DVD is accurate. And it is possible that the prints were not done as accurately as they wanted and what you are seeing on the print is actually an error rather than the correct colors. But I absolutely did notice it the theater when I saw the third movie. In my experience and knowledge, distribution prints are not done with the care and accuracy of color that the many talented people on this site tend to have. I’m more inclined to believe the scanned print is in error than there was some drastic change in artistic direction between the first and third movies.
You are right that one print isn’t a definitive record of the director’s choices, but there’s no reason to suspect it’s radically wrong. The print has a cohesive style, in that the scenes in the Matrix have a bleached out look compared to the real word (and quite a bit of green as well). It also has normal contrast and looks good, while the first DVD is weirdly washed out with it’s green-browns, which I think were quickly introduced during the telecine.
The two sequels (which were shot and produced together) do have a different style. They were also mastered on a Digital Intermediate, giving them a greater control of color, while the first one was colored optically.
I think the Wachowskis wanted to make the Matrix scenes more blanket green then they could satisfactorily do for theaters (or they changed their mind in time for the DVD). When the DVD/Laserdisc came out they took the opportunity to tint it during mastering. They then used a more blanket green for the sequels and then further revised the first film’s color to better match the sequels (The blu ray/2nd DVD is a full regrade with better contrast and control than the brown-green of the first dvd).