I actually never saw it in the theater. I was about 8 when the first one came out in 1974 and at the time I wasn't all that interested in musicals. I did see both of them in the late 70s or early 80s on TV.
By the way one of the sad facts about That's Entertainment is that it was the last film shot on the MGM backlot before it was demolished to make way for a residential development. By the time I was working at Sony in the early 90s the only thing left of MGM was the actual sound stages.
I think we may be dealing with two different topics here. First, not all 1.85 films are shot at 1.37. Many such films are/were shot with a hard matte in the camera so that the negative is already cropped at 1.85. However, what we are really dealing with here is how movies shot at 1.37 (or 1.33) were expanded to fill a 1.85 wide picture during some of the sequences in TE, both theatrically and on video. The physical size of the 1.37 picture has to be matted to 1.85 as you said, but then it has to be "blown up" (or enlarged) is order to reach the 1.85 width. Otherwise it would be no wider than it's original width. Softening of the picture almost always occurs when such enlargements are made (no different that having a small photograph from your pre-digital film camera enlarged to bigger and bigger sizes). It can easily be seen, for example, that footage from "An American in Paris" at the end of TE looks much sharper and clearer at its original 1.37 ratio but gets softer when enlarged to 1.85.
In any case, the movie is thoroughly enjoyable just as it was when I first saw it in 1974.
I understand the technical end of matting and ratios. My curiosity is the manner, shot by shot, this film was originally presented. I'm inclined to think that the DVD version is quite true to that. Yet, I've never been able to find a hard core definite account of the details.
Yes some films, although very few, are hard matted at 1.85:1, but that is simply an apature plate being used in the camera rather than in the projector.
But I think you are missing the point. The horizontal dimensions of a 1.37:1 frame are exactly the same as the dimensions of a 1.85:1 frame. The only difference is that the top and bottom of the frame are masked off to create the 1.85:1 aspect ratio. This is why you can sometimes find both a fullscreen and letterboxed version of the same film on DVD, and the image size is actually exactly the same. The fullscreen version just has the top and bottom mattes removed and you can sometimes see microphones and lights that should be covered by the matte.
Again the point is you can't "blow up" a 1.37:1 frame to 1.85:1 because the horizontal dimensions of the 35mm negative are exactly the same. If you were to blow up the image, the edges of the 1.37:1 frame would be outside of the 1.85:1 frame. You would not only not see the intended top and bottom of the original image but you would also lose the sides. Showing the full 1.37:1 frame with in the 1.85:1 dimensions would actually be reducing the image size to fit the matted frame, also known as piller boxing.
I think you are right in that the new video version is presenting the clips in the same way that the original release of the film did. In 1974 I doubt there would have been any thought of pillerboxing the old footage. In those days the mantra was "fill the screen".
I don't think it was until the advent of home video and letter boxing of wide screen films that there was any thought given to the idea that someone might want to see an older film in its original 1.37:1 aspect ratio in the theater.
In fact the first film that I know of that pillerboxed 1.37:1 film for presentation on a 1.85:1 screen was Fantasia in I believe its 1982 release.