No, the trend (and I'm generalizing from a small number of examples) is in the opposite direction; it's the small businesses or startups that use MySQL and produce better systems. Slightly bigger companies use Postgres and produce worse systems. Actually big companies use Oracle and produce terrible systems.
This could be a symptom of which businesses choose which databases. Large established businesses are probably going to prefer the commercially supported database, and are probably also going to have the resources to build impressive systems.