That's again exactly the technical detail fallacy the comment you replied to is arguing against. No, they are not making the "odd claim" you suggest. They suggest that laws make the difference when deciding about infringement. E.g. by explicitly excluding temporary copies created while watching as intended, where it doesn't matter how the OS and the browser handle the memory internally, but a thing that results in a file on disk the user keeps is clearly different. (Similarly to how software being copied into swap-backed memory while you run it is not an illegal copy, whereas copying the file elsewhere might)

Certainly with DRMed video it is common for the video to never be buffered/stored on disk. Sometimes a few seconds is, but even that is uncommon, and more likely it would simply be retained in RAM now.

With more secure DRM systems the OS literally never gets access to the video buffer, protected by hardware, in order to even send it to disk.