And the Lord God commanded the man, saying, “You may surely eat of every tree of the garden, but of the tree of the knowledge of good and evil you shall not eat... (Genesis 2:16-17 ESV)
In a legal sense the command includes anything from the tree, not just the most obvious, fruit; other parts of the tree such as leaves, flowers, bark, sap, and seeds would be covered.
While the first two violated the command relatively soon after it was given, the intent of the command was enduring. If they had not eaten the prohibition would remain in effect for future generations.
Suppose someone inadvertently, or intentionally served someone else something from the tree. Would the person who was served the prohibited part of the tree be guilty of breaking the command? If they were unaware of what they had been served were they guilty of breaking the command?
Far be it from you to do such a thing, to put the righteous to death with the wicked, so that the righteous fare as the wicked! Far be that from you! Shall not the Judge of all the earth do what is just?” (Genesis 18:25 ESV)
If someone unknowingly ate from the tree the Judge of all the earth would do what is just. The essence of what the man says speaks to this legal aspect of the command: does it apply to something someone else removed from the tree?
Now it is clear from the events described that Adam knew where the fruit he ate came from:
So when the woman saw that the tree was good for food, and that it was a delight to the eyes, and that the tree was to be desired to make one wise, she took of its fruit and ate, and she also gave some to her husband who was with her, and he ate. (Genesis 3:6 ESV)
The man said, “The woman whom you gave to be with me, she gave me fruit of the tree, and I ate.” (Genesis 3:12 ESV)
The man's appeal is not so much as to blame the woman as an attempt to say he did not violate the command. "Yes I ate what came from the tree, but I took from the woman." The implication is that on some level "I" did not violate the command because "I" did not take from the tree.
Adam did not lie. He told all of the truth: he ate what came from the woman. Perhaps he had a good attorney or a good legal mind and so is hopeful he will be let off on the legal technicality that he ate what was taken from the woman. Perhaps he is like Abraham who hopes only that the Judge of all the earth will do what is just and be shown mercy in that in the very strictest sense of interpreting the command, there is room for leniency. After all it is true that he did not eat from the tree.
It is true the man violated the command as it was given to him. However, for a command that was to be passed on to future generations, especially if the population grew to cover all of the earth, taking directly from the tree becomes an integral part of the command.