I want to talk about a practice in which you are obliged to cite trustworthy people or publication to discuss a topic, in contrast to merely talking about things that do not have original reason to be true--just guessing or common sense. I know already that speaking with reference is not an appropriate phrase for that but I just mentioned it in the title to be able to communicate the meaning I want. I guess a related appropriate phrase for me is speaking with credibility but this phrase does not explicitly mention the practice of citing references. I want something that does
If memory serves, my post-graduate professors used a few ways to describe what you're trying to say.
First, like @NVZ mentioned in the comments of your question, one possibility would be to speak authoritatively, which implies credibility through support of documentary evidence and the acceptance of authorities in the field.
Additionally, I remember a phrase used by a post-graduate professor of mine. She warned us that we must speak with the weight of impeccable research or end up failing her class. This explicitly mentions the presence of research, and that such research is NOT vulnerable to attack, denial, or excuse (meaning that the research is objectively sound, logically valid, and absolutely accurate).
Still, while both phrases imply the presence of supporting evidence and citation, neither phrase explicitly mentions them.