In 9:1, the first passuk of the parsha, the Torah tells us, "And it was on the eighth day Moshe called to Aharon and his sons and to the elders of Israel."
Rashi tells us that he did so in order to make sure everybody knew that Aharon entered the Mishkan and served as Kohen by the order of Hashem and not on his own decision.
I find it amazing that after all that has happened until now and after the constant testimony by Hashem in the Torah that Moshe and Aharon performed specifically according to the directives from Hashem, he is still under suspicion. there still needs to be outside confirmation that Aharon is acting faithfully and not on his own initiative.
What does he need to do already for people to trust him and not think he is pulling a fast one?
The lesson, I think, is that nobody is above suspicion. Everybody must behave in a way that raises them above any possible suspicion. Nobody should assume they have people's trust and if they do something, even if it looks questionable they will still have people's unwavering trust and support.
People are naturally skeptical about others, especially about leaders. Leaders must be careful to act in ways that keep them above suspicion. Aharon and Moshe were careful to do so.