I don't think the claim of MySQL replication being better is related to statement vs. row vs. binary diff. I think it is about the tooling and community knowledge about replication, and about running MySQL in large scale production environments in general.
MySQL is run more often at extremely large scale (Facebook, YouTube, Twitter, Dropbox, etc.) than Postgres. That results in very battle tested and/or featureful tooling like orchestrator (https://github.com/github/orchestrator), MHA (https://github.com/yoshinorim/mha4mysql-manager), ProxySQL (http://www.proxysql.com/), and gh-ost (https://github.com/github/gh-ost), along knowledge and best practices shared by those organization.