I'd say needing to read the documentation for the first time is what bumps it up from low complexity to medium. And then at medium you should still do it if there's a significant cost difference.
I think if it were true that the tuning is easier if you run the infrastructure yourself, then this would be a good point. But in my experience, this isn't the case for a couple reasons. First of all, the majority of tuning wins (indexes, etc.) are not on the infrastructure side, so it's not a big win to run it yourself. But then also, the professionals working at a managed DB vendor are better at doing the kind of tuning that is useful on the infra side.