That's incorrect. Dotcloud ran both stateless and stateful services on the same container fabric, unlike Heroku and every other PaaS. Specifically you could run a managed containerized postgres, mysql, mongodb, redis, rabbitmq, and custom stateful tcp services. Docker was a result of that design.

Docker was specifically designed to NOT impose a model of ephemeral containers. For example, by default 'docker run' preserves all data.