Clearly they do not yet have a yottabyte worth of data. It would be silly to build a warehousing site like that and have it be full-up with data the day it first opens for business.
I expect these sizing claims (which presumably come from some sort of government statements about the facility) are based on a timeline on the order of ten years or more. A YB in 2024 is going to take a lot less physical space than a YB in 2014.
You'd need a 2-3 order of magnitude increase in storage density to get anywhere near reasonable. I suspect that's not going to happen in 10 years but I don't know the current and projected rates of storage density increases.
Based on that, it sounds like the yottabyte claims refer to raw, unprocessed data collected. Off the bat, I'm willing to believe in a 2 orders of magnitude decrease after data reduction techniques are applied to the raw data. My experience with data collected from telescopes was that we got about 100:1 reduction on the raw data versus what went into permanent storage.
The San Antonio site was news to me, though obviously no big secret since that book was published years ago.
I expect these sizing claims (which presumably come from some sort of government statements about the facility) are based on a timeline on the order of ten years or more. A YB in 2024 is going to take a lot less physical space than a YB in 2014.