Yes.
I'm aware.
However, the peerage can be inherited so even if they are supposed to be independent now, they are still likely related to a royal line somewhere.
For examples:
- The Duchies of Russia (including Muscovy) are supposed to be related to Prince Rurik, who is in turn supposed to be from a Scandinavian royal lineage (Denmark, Sweden, or Norway).
- Luxembourg was elevated to a Duchy by Emperor Charles IV of the Holy Roman Empire (who came from the Luxembourg dynasty itself).
- House Babenberg had close ties to Ottonian dynasty of the Holy Roman Empire and became a Margraviate (recognized as a more directly related house of the royalties) by Emperor Otto II before eventually elevated to the Duchy of Austria by Emperor Frederick I.
The only example you mentioned that really fits into the "independent Duchy" is Lithuania. And I do recognize this fact.
Lithuania in that sense is supposed to be completely independent before their title of a Grand Duchy because their first rulers were not related to any European royal lines and became Grand Dukes through military prowess and tribal leadership. Though, the title coming from either succession or usurpation of tribal federation leadership or a centralized kingdom makes that very much arguable, if I were to comment on it.
Regardless, the sons of a Duke (Archduke, Grand Duke too) can be considered to be Princes, if they are in line to succession of the royal lineage (as in related by blood to royalties).
Well, it's not strict a rule since the Holy Roman Empire had Dukes who were non-royalties given Princely ranks, which in turn making their sons Princes too.
In short: it's damned complicated and yes, I realized I didn't exactly make the correct statement about the ducal status the first time. And I apologize for it.