The article could be summed up as "Postgres is not a distributed database." MySQL isn't either, although it certainly has more friendly replication technology. I think it's a lot more likely that what's really happening here is that they've designed their "schemaless" schema or its supporting software to handle the kind of soft errors that MySQL is permitting and Postgres was not.
We have MySQL replication across the country where I work and I certainly wouldn't characterize it as robust; it fails every 3-6 months. MySQL replication is certainly a lot older and easier to use than Postgres's, but SQL databases are fundamentally CP systems. When you say "This design means that replicas can routinely lag seconds behind master, and therefore it is easy to write code that results in killed transactions" it sounds like you're blaming the way replication was implemented for a physical problem. There is no way to design a replication system such that two highly-consistent databases can achieve perfect availability in the face of real-world networks. A worse protocol can exacerbate the problem, but a better one can't make it go away.
I have never seen corruption with Postgres (unlike MySQL), but I have never tried cross-datacenter replication with it. Apart from that, Postgres generally seems to do much better with consistency than MySQL does, where DDL statements are not transactional, etc. So I am not surprised to hear that their system trips harder on Postgres's more aggressive consistency.
In short, I suspect a more robust solution to their problem is a NoSQL database. On the other hand, it sounds like they want a combination of availability and consistency that will be difficult to get off-the-shelf. I'm glad they found a way to make it work. I wouldn't generally choose Postgres for a scalable system with an aggressive availability constraint--but then again, I wouldn't choose MySQL either, and I generally avoid problems that demand highly scalable, highly available solutions.