You are right, in verse 4:

Then the serpent said to the woman, “You will not surely die. 5 For God knows that in the day you eat of it your eyes will be opened, and you will be like God, knowing good and evil.”

But my point was God never said the tree could not be touched, just not to eat of it. Eve added that the tree was not even to be touched, so basically she added to God's word.