You are correct, God's word needs to be delivered with accuracy, however, the point being if a false prophet did confess and repent, that person would not lose their salvation over it, anymore than a christian reading and preaching the word of God incorrectly from scripture would if they saw their error at some point and repented of it. (which we all have done...or have we?)
"Are the non-repentant still safe in grace?" You tell me. If someone is angry at his brother, but believes correctly everything else that God speaks, are they safe? That is God's call, because He sees the intent in all things, which we don't. You can't watch a youtube video and "know" what is going on in that person's heart since they last made a false statement. Only God knows. Those people's mistakes will be broadcasted forever to the day they die and beyond. We may never know their true heart on the matter since we don't know them personally. I think that is one reason most of our churches will not make videos or be on TV, radio, because once people hear what you have to say and record it, you must live with your mistake forever repeatedly condemned.