That’s essentially correct but not always. Some elders or authorities are nearly always “sie” and small children are nearly always “du” but it’s very easy to find yourself in a seeming gray area, getting it wrong and insulting some burgher or hausfrau by sounding too distant (snobbish) or seemingly treating them like a child. Obviously I never fully mastered it despite a semester of immersion in Trier.
Like incorrect grammar in any language although Germans seem a little more sensitive. Lots of nuance and situational stuff...declension, gender etc. (We have only one “the”!)
2 years in high school and one year in college. Stationed in WesT Berlin in ‘60’s. Maintained a basically C level of proficiency for the Air Force. Been many years since those days.
Must have been a great experience at Universität Trier!
Actually, it's even more nuanced.
Speaking to a noble lord: Ihr (2nd Person Plural Intimate = the standard way of addressing a plurality of children, family members, close friends, etc.); the Possessive is "Euer" - hence, "Ihr ergebenster Diener" - your humble servant. But also still used in some dialects, e.g., when an old market woman addresses me, an obviously high-class person.
Speaking to a coachman or other subservient person: Er or sie: Er bringt mir meinen Hut und Gehstock! = "Bring me my hat and cane!" (Literally: "He brings me...")
Ich verbleibe
Euer ergebenster Diener!