Bit rot can exist on HDD platters, flash/SSD drives, DVDs and Blu-Rays (even more so with DIY burnable discs than pressed ones)... flash/SSDs are theorized to have up to 10 year data retention, in ideal conditions. An EMP wipes out anything magnetic so if NK launches a shiny happy nuke say "toodles" to the radius where the bomb goes splodey over... there's a reason why countries around NK have more concerns than California...
So the probability is, in 300 years, all the cat videos will be safe. Due only to redundancy and only if major cat-astrophe doesn't happen.
And there's no way humanity can go back to the 1000s, one way or the other.