I am suspicious that, while I have never heard it read this way, part of how the Melchizedek priesthood holds "the keys of the mysteries of the kingdom" is in that it has power to bestow the gift of the Holy Ghost. I recently pointed out to my children that in D&C 76, which Joseph Smith referred to as "the vision" thereafter, it says that they were "in the spirit" and the vision began when "by the power of the spirit our eyes were opened".
That is, it doesn't say the vision required an angel to appear to initiate it, or that it required the priesthood. It required the gift of the Holy Ghost. And while it would not be revealed to the church by anyone who was not in a position of authority over the church, it could literally be shown to any man or woman who had the gift of the Holy Ghost.
Which fits with something else Joseph Smith taught, which Elder McConkie nicely summarized, saying: "But what counts in the field of religion is to become a personal participant in it. Instead of reading all that has been written and evaluating all that all the scholars of all the world have said about heaven and hell, we need to do what the Prophet said: gaze five minutes into heaven." (Bruce R McConkie, "How to get personal revelation")