Certainly that dev guy had it hoplessly wrong, but you too have it wrong - not hopelessly wrong, but somewhat wrong.
During much of my career I've had customer support people, ops people, and development people working for me and an important part of my job has been to ensure that those disparate groups with differently centered skill sets do indeed act as a unified team rather than pulling in different directions.
Teams are like sets - they can be joined together to make larger teams, which in turn can be joined together to make still larger teams, and so on until maybe at some point you get to a unit that's too big to behave as a team. If communications between the diferent small teams are adequate, they will effectively become a single team (and will be many times as effective as if they dont). That certainly doesn't mean that sysops or any part of it (such as production operations dbas) are going to be subordinated to development, or that development is subordinated to customer support, or any nonsense like the Dev you describe was promoting, but it certainly does mean that all these different skills (and other functions, like license management, supplier relations, technology research, data protection conformance, avoiding conflict of interests, and so on) must work together as a team (or communicate so effectively that you can't detect that they aren't all working together as a team, which I don't really believe is any different from actually being a team) if they are to be really effective.