I'm not sure they've sampled enough videos to be able to make that kind of central limit theorem assertion. A trillionth of a percent is an awfully small sample of the total space.
How did you get the trillionth of a percent? The total space is 2^64 and they found 24,964 videos. Based on their estimated number of videos (13,325,821,970) we can infer[1] that they have made the equivalent of a sample of size 3.46e13. I say equivalent because of the "cheating" they mention in the article which improves the efficiency of their method so their actual sample would be 32000 times smaller I guess). Anyway as shown in the link below that's a good sample size since it gives a precision of about 0.6%.
[1] https://news.ycombinator.com/item?id=38744227