How can they possibly guarantee eleven nines? Considering I’ve never heard of this company and they offer such crazy-sounding improvements over the big three, it feels like there should be a catch.
11 9s isn't uncommon. AWS S3 does 11 9s (upto 16 9s with cross region replication?) for data durability, too. AFAIK, AWS published papers about their use of formal methods to ascertain bugs from other parts of the system didn't creep in to affect durability/availability guarantees: https://blog.acolyer.org/2014/11/24/use-of-formal-methods-at...
Those numbers probably aren't as absurd as you think. 16 9s is, I think 10 bytes lost per exabyte-year of data storage.
There's perhaps the additional asterisk of "and we haven't suffered a catastrophic event that entirely puts us out of business". (Which is maybe only terrorist attacks). Because then you're talking about losing data only when cosmic-ray bitflips happen simultaneously in data centers on different continents, which I'd expect doesn't happen too often.