Maybe. The question is why are we needing to read these disks in a thousand years. I would guess right now that the most likely case is information we care about is archived on modern formats such as hard drives, which are constantly being copied to different drives as the old ones go out and so in a thousand years they'll still have all the data in a much more accessible format than a very obsolete disk.
If, instead, we are talking about some human disaster and, that constant copies is lost at some point, we're kind of stuck. I don't think the technology to read those disks will exist either, even though in theory, yes, that could be done. It would be a massive reverse engineering effort and I don't think they will even know to start doing that with these weird disks that the agents had.
If you want something archived for a thousand years, well, we know that clay tablets baked worked, although we sometimes can't read the letters but at least seeing something with the eyes says there's something and if there's enough of them we have decoded language.
The best archival paper in ideal conditions lasts more than a thousand years, but in more typical storage, we can't store paper that long. Paper has only been stored successfully in Egypt for that long. I'm sure there are other deserts though that would count just as well.
Issue with storage is you need shelf stability without ongoing electrical/mechanical work refreshing data time to time. Masked ROMs and M-Discs are those two things which can really last a very long time; Floppies, Hard Disks, Solid State Storage and present day ROMs all require periodic costs, efforts and refreshes to keep them going (that means they can't be kept in storage and then re-opened in 30 years).
We also need a mechanism that outlasts that archival lifespan so how to read Discs or Masked ROMs and how to interpret them, also needs to be stored as well. Repairing electronics is a valuable skill that needs to be passed on across generations as well.
Keeping humans around seems to be the best bet, given how things are going, I wouldn't count on the present set of beings around to preserve any of this information that well either.
I think 1,000 years maybe doesn't matter that much. However, these predictions are imperfect. If they're aiming for 1,000 years, that makes me more confident the disc will be readable in 100 years, which may matter more.
> The question is why are we needing to read these disks in a thousand years.
The British Domesday Book from 1086 is still referenced by historians for all sorts of purposes:
* https://en.wikipedia.org/wiki/Domesday_Book
Not sure what kind of present-day data the historians of the future would be interested in.
> If you want something archived for a thousand years, well, we know that clay tablets baked worked […] The best archival paper in ideal conditions lasts more than a thousand years, but in more typical storage, we can't store paper that long.
Well, paper would best be stored in a fairly dry place, so deserts may be a starting point.
Generally the only institutions / organizations that have managed to survive for centuries / millennia have been monasteries. Temples/churches have often been close to communities for public worship, but most religious traditions seem to have groups of individuals that were a bit more 'removed' from society at large. Organizing around such things could be attempted (a plot point in Stephenson's Anathem.)
Generally burying stuff and leaving clues so that an 'advanced enough' society can unbury it at some point may be another idea.