Did Eve really do this?

I have heard dozens of messages about how Eve, during her conversation with the serpent in Genesis 3, added to the Word of God. They obviously compare the following passages:
Genesis 2:16 And the LORD God commanded the man, saying, Of every tree of the garden thou mayest freely eat:
17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.

Genesis 3:2 And the woman said unto the serpent, We may eat of the fruit of the trees of the garden:
3 But of the fruit of the tree which is in the midst of the garden, God hath said, Ye shall not eat of it, neither shall ye touch it, lest ye die.

It is very important to get the timeline down in this account of creation and the fall of man. God creates man; God gives man a specific command; God creates woman.

God clearly told Adam that he was not to eat of the tree of the knowledge of good and evil. This command was clearly given before the woman was created. There can be no doubt that Adam, after Eve was created, was responsible to instruct her in the commands of God. It also seems to be clear that he did tell her what God said. Adam undoubtedly told Eve that God told him that they were not to eat of that particular tree. They could eat of any other tree in the garden, just not that tree.

Now, here is where I would like to speculate just a bit. There is no way that I or anyone else can be dogmatic about this, so let me offer just a few thoughts about this incident.

It is possible that Adam, as the God-given authority in the home, instituted his own safeguards to see that his wife stayed a safe distance from violating the clearly stated law of God.

It is possible that Adam told his wife, "God said that we are not to eat of this tree” and then went a step further and added, “And I do not want you to even touch it!” Let’s face it, it would have been very difficult for Eve to eat something if she'd never even touched it.

There is no disputing the fact that Eve said to the serpent when he asked what God had said: “God hath said, Ye shall not eat of it, neither shall ye touch it, lest ye die.” Could it be that Eve was repeating Adam’s command as if it were the command of God? That would be very much in keeping with the Word of God in
Ephesians 5:22 Wives, submit yourselves unto your own husbands, as unto the Lord.

I believe that it is very possible that Eve, until this great face-to-face temptation with Satan himself, submitted to the authority and protection of her husband, even to the point that she repeated Adam’s command as if it had come God Himself.

Consider this, if Eve would have been guilty of adding to God's Word here, would not that have been a sin? Maybe, just maybe, this was not a sin because she was simply submitting to Adam, her God-given authority. If it were a sin, would there have been any need to eat from the tree? Would not mankind have been plunged into sin by this simple act of adding to God's Word? Again, I am not being dogmatic, just sharing some thoughts that I have mulled over recently.