“Anbaʾanī” originally means “he informed me,” and earlier hadith scholars could use it near-synonymously with akhbaranī. Some later scholars reserved it for transmission based on ijāzah. Certain later contexts also used “ʿan” when permission rather than direct hearing was intended.
The historical usage matters. A student granted permission to transmit a book has not thereby personally heard the text from the teacher's voice; a formula ought to preserve that distinction.
Critical rule: interpret technical expressions by the narrator's era, habits, and available contextual evidence. “Anbaʾanī” does not unconditionally establish either direct samāʿ or ijāzah in every period.