How do we know that they did 1080p scans of the films back in the early 2000's? All that we know is that Paramount, at most, scanned them with HD Broadcast standards in mind (especially since at the time there was nothing for Blu-Ray or HD-DVD, and DVHS was barely making an impact). So for Paramount doing even just a 720p transfer in the early 2000's would've been sufficient, as far as they were concerned.
Not 1080 scans, 1080 telecines. An HD telecine can be up to 1080 horizontal lines of vertical resolution and is output to tape (HDCam or D5). Scanning, on the other hand, can be anywhere from 2K to 8K and isn't output to tape, it's output to digital files. Telecine is a real-time process, because it's basically an HD camera that's aimed at the film as it goes through what is essentially a projector. A film scanner is a slower process, it scans each frame separately in red, green, and blue light.
And we know they had 1080 line HD telecines for quite some time because, well, 1080i versions of the films have been floating around newsgroups since about the mid-2000s -- that's when I got them anyway. I think HBO-HD and Cinemax-HD have been showing the first six films since they began broadcasting in high-definition (HBO in 1999 and Cinemax in 2003).
And again, you can see DNR-free clips from these older 1080 line telecines (which were the basis for the I & III-VI Blu-rays) on the new HD special features.