Great info, although I don't agree at all on only keeping one budgie. I would strongly discourage it. In fact it's even illegal where i live due to animal welfare issues.
If your birds lose their tameness because you keep 2 or more, that's a clear sign you weren't spending enough time with them in the first place, i'd say.
I've always kept budgies in pairs/flocks of 2 or more, and would never dream of keeping them alone. They are way more active and happy that way since, as you already said, they are highly social animals. There's a clear difference in the wellbeing of singly kept birds vs. birds that live with other budgies. (Studies show less stereotypic behaviour, more healthy behaviour, more playbehaviours and less indicators of stress in budgies not kept singly.) All my budgies and tiels have been parent fed, flighted, kept in pairs or small flocks, were very tame, some trick trained, and they all loved to hang out with me.
That's the most common setup in sweden as a whole, and there's no shortage of wonderful pet budgies here.