Correct.
And for us people who believe God is immutable, we have peace knowing that God will not change His mind about it.
You are making immutability a fixed attribute like eternality or omnipresence (metaphysics). Issues of faithfulness are in the philosophical arena of volitional morals. God is faithful because He chooses to be, not because He is a preprogrammed robot with no ability to keep His Word. God's character is not automatic. We have no reason to not trust God and His Word. If you can trust the word of your parents, how much more can you trust the Heavenly Father based on His self-revelation and track record.
Man and Satan are not trustworthy. God is not a man or devil.