That was my impression the first time I watched it, as well. That said, I think Chibnall disagrees with you.
It was the only interpretation consistent with the explicit statement in "The Three Doctors" years before that Hartnell was the earliest Doctor, as well as later references confirming it in "Mawdryn Undead" and "The Five Doctors." So it was always strange to me that some people thought they were earlier Doctors rather than earlier Morbii.
At least Chibnall's retcon rationalizes the inconsistency by having them be secret earlier incarnations, so the characters who said Hartnell was the first (the Time Lords in "The Three Doctors" and the Doctor himself in the later instances, plus all the references in the modern series prior to last season) were stating the truth as far as they knew it.