Do animation studios like Pixar, Dreamworks, and Disney use super-sampling? Does any of their rendering techniques involve rendering an area at a higher resolution just to scale it down in order to mitigate artifacts? I know they use ray methods rather than rasterization however ray methods still have artifacts even when done with a ton of rays.. right?

I noticed a few moments in the film Moana that seemed to be poorly rendered because small details seemed fuzzy and sorta pixelated. Especially around the edges of a figure that was in focus with a slightly blurred background. Could they have used supersampling on those scenes to decrease the issue?
Super-sampling for ray-tracing doesn't just mean rendering an area at higher resolution and then downscaling the finished image: in fact, this simplest super-sampling technique is really not effective enough for high-quality production rendering.

In a production ray-tracer, super-sampling means sending more than one primary ray per pixel (16 primary rays per pixel is a good average) and then using signal reconstruction techniques (i.e. not just averaging) to compute a colour for each pixel of the image. Using lots of primary rays doesn't just help to avoid aliasing (jaggies) from when polygons partially cover pixels; it also helps to smooth over noise added in shading, such as when sampling global illumination or fuzzy reflections.

In addition, super-sampling by sending more rays lets you jitter the sample positions to avoid the artefacts you get from regular sampling. It also lets you use the results of previously traced primary rays to decide where to put more samples.

For example, the simplest adaptive sampling algorithm is contrast based: within each pixel, you measure the contrast among all of the primary rays. Pick the pixel(s) with the highest contrast, and shoot more primary rays in those pixels. You can also use the contrast between samples to choose where in the pixel to shoot new primary rays, but then you have to use a more complex reconstruction algorithm to avoid bias in your result.

If you can find a frame-grab of the particular details you noticed, it would be possible to go discuss those in more detail. It's entirely possible that some artefacts are caused by a particular technique, and aren't related to super-sampling at all.