squeaky, you are so right. Any psychologist who said that would be an idiot who doesn't understand family structures. I was certainly brought up in a family where the adults were in charge. We were loved and prioritised but there was absolutely no need for us to be treated exactly the same way as the parents. My mum prioritised loving us, educating us, disciplining us. Not making sure we were feather-bedded.
My dad too. And my parents were divorced so there were some tough choices to make. For years we slept on camp beds for weekends at my dad's flat. My Dad didn't. Did that mean we weren't important? No. It meant we were kids and it was fine.
My self-esteem is very robust - and that's precisely because of the clarity I had as a child which was of the "I'm the parent, I'm in charge, you're the child, I will decide what happens and you can trust me to get it right" variety. That did not mean getting everything that mum got. That would just be weird.