My sense is that companies choosing to use Postgres are more likely to have dedicated DBA's before Postgres is deployed. In these companies the move to Postgres is often DBA-initiated.
In general, though, DBA can mean a bunch of things. It can range from a dev-ops kind of role to something like a sysadmin kind of role and a bunch of things in between. One thing I think we see industry-wide is that strict specialization in DBA tasks seems to be on the decline and for good reasons. It is a move I think from a strictly parts-oriented, details-centric operations approach to a big-picture, approach where the ability to communicate across teams is helpful.
Also regarding the BIG users of Postgres, the DBA-like people I have known who have worked there have been part-time DBA's and part-time C programmers doing things like porting Postgres to new platforms or building new replication systems. As far as I can tell, the dedicated "nothing-but-a-dba" is something that exists mostly waning.
