All transgressions, (acts done without knowledge or full understanding), are covered through the Atonement and the Law of Azazel and do not even require a knowledge of Jesus Christ or the atoning sacrifice to have full efficacy.

However, those who actually commit sin must accept and apply His At-One-Ment into their lives by refusing to allow the innocent to suffer for their sins. This then flows forward from them to all people and generations to come and their acts which are truly sins are absolved through their having come to the necessary love and charity for the atonement to be in full force in their lives. And thus, they are truly... Saved. As they save all, so too shall all save them also. And thus the Love of Christ will fill the lives of all.

33 But God did call on men, in the name of his Son, (this being the plan of redemption which was laid) saying: If ye will repent, and harden not your hearts, then will I have mercy upon you, through mine Only Begotten Son;
34 Therefore, whosoever repenteth, and hardeneth not his heart, he shall have claim on mercy through mine Only Begotten Son, unto a remission of his sins; and these shall enter into my rest.

Eighth Hebrew letter: Chet Numerical value of eight. Pictographic meaning wall, fence, protect, new beginning, separation, sin, outside, olam haba. - https://graceintorah.net/2015/06/15/hebrew-numbers-1-10/

Alma 12:33 But God did call on men, in the name of his Son, (this being the plan of redemption which was laid) saying: If ye will repent, and harden not your hearts, then will I have mercy upon you, through mine Only Begotten Son;
34 Therefore, whosoever repenteth, and hardeneth not his heart, he shall have claim on mercy through mine Only Begotten Son, unto a remission of his sins; and these shall enter into my rest.

Alma 29:5 Yea, and I know that good and evil have come before all men; he that knoweth not good from evil is blameless; but he that knoweth good and evil, to him it is given according to his desires, whether he desireth good or evil, life or death, joy or remorse of conscience.

Alma 32:19 And now, how much more cursed is he that knoweth the will of God and doeth it not, than he that only believeth, or only hath cause to believe, and falleth into transgression?

Mosiah 3:11-12 For behold, and also his blood atoneth for the sins of those who have fallen by the transgression of Adam, who have died not knowing the will of God concerning them, or who have ignorantly sinned.
12 But wo, wo unto him who knoweth that he rebelleth against God! For salvation cometh to none such except it be through repentance and faith on the Lord Jesus Christ.

D&C 29:49-50 And, again, I say unto you, that whoso having knowledge, have I not commanded to repent?
50 And he that hath no understanding, it remaineth in me to do according as it is written. And now I declare no more unto you at this time. Amen.

Moroni 8
8 Listen to the words of Christ, your Redeemer, your Lord and your God. Behold, I came into the world not to call the righteous but sinners to repentance; the whole need no physician, but they that are sick; wherefore, little children are whole, for they are not capable of committing sin; wherefore the curse of Adam is taken from them in me, that it hath no power over them; and the law of circumcision is done away in me.
...
10 Behold I say unto you that this thing shall ye teach--repentance and baptism unto those who are accountable and capable of committing sin; yea, teach parents that they must repent and be baptized, and humble themselves as their little children, and they shall all be saved with their little children.
11 And their little children need no repentance, neither baptism. Behold, baptism is unto repentance to the fulfilling the commandments unto the remission of sins.
12 But little children are alive in Christ, even from the foundation of the world; if not so, God is a partial God, and also a changeable God, and a respecter to persons; for how many little children have died without baptism!
...
19 Little children cannot repent; wherefore, it is awful wickedness to deny the pure mercies of God unto them, for they are all alive in him because of his mercy.
...
22 For behold that all little children are alive in Christ, and also all they that are without the law. For the power of redemption cometh on all them that have no law; wherefore, he that is not condemned, or he that is under no condemnation, cannot repent; and unto such baptism availeth nothing.

Galatians 3:19
19 Wherefore then serveth the law? It was added because of transgressions, till the seed should come to whom the promise was made; and it was ordained by angels in the hand of a mediator.

Romans 3:20
20 Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin.

Romans 2:12
12 For as many as have sinned without law shall also perish without law: and as many as have sinned in the law shall be judged by the law;

Romans 5:13
13 (For until the law sin was in the world: but sin is not imputed, (assigned), when there is no law.

Amonhi’s response if very good, and right on point. There is an implication for the presentation in the book. In a quick search for “sin” and “transgression” I found:

Mosiah 3: 11 For behold, and also his blood atoneth for the sins of those who have fallen by the transgression of Adam, who have died not knowing the will of God concerning them, or who have ignorantly sinned.

This seems to counter the claim made in the book. Amonhi suggests that these two words are not always used precisely by authors/translators of the scripture. Thus, Amonhi’s discussion of the need to infer from context whether it is actually sin or transgression being discussed should probably be in the book.

I know it would be cumbersome, but in the book it might make sense to choose words that would not conflict with the scriptures. For example, use “accountable sin” for those actions where we have sufficient knowledge, etc. to be accountable. Use sin/transgression for the others. Then, you would be completely consistent with scripture.