I have an alternate understanding: Keys are only authority in that they are knowledge.
When we possess knowledge, we have power to act differently.
And this greater priesthood administereth the gospel and holdeth the key of the mysteries of the kingdom, even the key of the knowledge of God. ~Doctrine and Covenants 84:19
Woe unto you, lawyers! for ye have taken away the key of knowledge: ye entered not in yourselves, and them that were entering in ye hindered. ~Luke 11:52
Howbeit that was not first which is spiritual, but that which is natural; and afterward that which is spiritual. The first man is of the earth, earthy; the second man is the Lord from heaven. As is the earthy, such are they also that are earthy; and as is the heavenly, such are they also that are heavenly. And as are the records on the earth in relation to your dead, which are truly made out, so also are the records in heaven. This, therefore, is the sealing and binding power, and, in one sense of the word, the keys of the kingdom, which consist in the key of knowledge. ~Doctrine and Covenants 128:14
Now the great and grand secret of the whole matter, and the summum bonum of the whole subject that is lying before us, consists in obtaining the powers of the Holy Priesthood. For him to whom these keys are given there is no difficulty in obtaining a knowledge of facts in relation to the salvation of the children of men, both as well for the dead as for the living. ~Doctrine and Covenants 128:11
What was the whole focus of the events in the Garden? That Adam and Eve would gain knowledge. That they would have a key to unlock (or sufficient knowledge to understand and grow from) the fullness of life experience. That knowledge was the most powerful thing they could possibly possess. Satan had advantage over Eve in the garden (the ability to beguile her) because he had more knowledge than she did.
Joseph Smith also used the word key in terms of knowledge (I can't find a source for this at the moment--anyone remember?). In teaching how to understand revelation, he said the key was to ask yourself what question the revelation is answering. That stuck in my mind because his use of the word "key" was only in reference to knowledge, and not in reference to authority as it is used today.
Joseph also taught that those who have more knowledge have more power:
"A man is saved no faster than he gets knowledge, for if he does not get knowledge, he will be brought into captivity by some evil power in the other world, as evil spirits will have more knowledge, and consequently more power than many men who are on the earth. Hence it needs revelation to assist us, and give us knowledge of the things of God." (History of the Church, 5:588.)
Knowledge is power. "Key" is another word to express knowledge that brings power.
And I can say, in my life, knowledge of the Truth--including that Jesus, Himself, IS the Truth--has been the key to unlocking the emotional and spiritual prison I've lived in for decades.