This is absolutely true and very correct
Being authentic is a lens through which your audience will view your intent. If you aren't authentic, then you have bad intent and your audience will absolutely figure that out. You should really enjoy what you do and love whatever it is that you're talking about. If you don't, then you're not being authentic with your audience and that is a lose-lose situation for everyone.
Authenticity is all that matters in life and in business, like you wrote above, even people will get to forgive us when we err but remain authentic in it,
I remain myself always and don't dont loose or adjust my authenticity when I come across people.