Josephine's evidence, a solemn declaration of a fact upon oath, is strong evidence that her mother said that she (Josephine) was the daughter of Joseph Smith. Josephine had first-hand knowledge of what her mother said.
The existence of the affidavit clearly leads to a significant increase in the weight that can reasonably be given to the hypothesis that
(a) Joseph Smith was Josephine's father
and rather more to the hypothesis that
(b) Joseph Smith had sex with Josephine's mother (but she may have had sex with other people too, so Joseph Smith may not have been Josephine's father)
and more still to the hypothesis that
(c) Joseph Smith was generally assumed to have sexual relations with his plural wives, so that Josephine being his child was a reasonable possibility.
I am positive that if an affidavit existed attested to the opposite, ie, that Joseph Smith did NOT have sex with his polyandrous wives, that defenders of the faith would be declaring "victory".
Considering how reticent these women were to discuss this issue, the fact that we have any evidence of these polyandrous relationships is significant. It was difficult enough for these women to accept polygyny; accepting polyandry would have been that much more difficult, particularly knowing how society would react. Even when being questioned by friendly witnesses, they were reticent:
http://www.wivesofjosephsmith.org/09-Ma ... ghtner.htm
Mary Rollins first met Joseph Smith in early 1831. She and her family were new converts and Joseph Smith had just arrived in Kirtland from New York state. Twelve-year-old Mary remembers, “when he saw me, he looked at me so earnestly, I felt almost afraid [and I thought, ‘He can read my every thought,’ and I thought how blue his eyes were.] after a moment, or too he came and put his hands on my head and gave me a great Blessing, (the first I ever received)”. Joseph also prepared Mary for their eventually marriage: “[He] told me about his great vision concerning me. He said I was the first woman God commanded him to take as a plural wife.” In the fall of that year, Mary and her family left Kirtland for “Zion”, which was being established in Missouri.
Three years later, Mary and Joseph would be reunited when Joseph led the Zion’s Camp expedition from Ohio to Missouri. Mary remembers, “In 1834 he was commanded to take me for a Wife, I was a thousand miles from him, he got afraid”. At the close of Zion’s Camp, Joseph returned to Kirtland. Mary stayed in Missouri, living in Liberty and Far West. Perhaps thinking her marriage to Joseph was off, she married Adam Lightner in 1835. By 1840 they had settled in Nauvoo, and were raising two children.
Early in 1842, Joseph approached Mary about becoming his wife. According to Mary, Joseph said, “The angel came to me three times between the year of ’34 and ’42 and said I was to obey that principle or he would slay me.” Furthermore, Joseph told her, “I was his before I came here and he said all the Devils in hell should never get me from him...” and “I know that I shall be saved in the Kingdom of God. I have the oath of God upon it and God cannot lie. All that he gives me I shall take with me for I have that authority and that power conferred upon me.”
Initially, Mary did not accept Joseph’s proposal. She wanted a witness from God. Mary recalls, “If ever a poor mortal prayed I did”. By February 1842 Joseph had convinced her it was a correct principle and she, “went forward and was sealed to him. Brigham Young performed the sealing...for time, and all Eternity.” Mary said her husband Adam was “far away” out of town at the time of her marriage to Joseph.
Mary continued to live with her first husband, Adam. Of this arrangement, she later wrote, “I could tell you why I stayed with Mr. Lightner. Things the [current] leaders of the Church does not know anything about. I did just as Joseph told me to do...”
After Joseph Smith was killed in 1844, Mary and her first husband Adam continued to live in Nauvoo and the Midwest. In 1863 they moved to Utah. In her elderly years, Mary wrote to an acquaintance, “...I Love to talk about the Prophet and the Early days of the Church [I] will always remember how Joseph looked...at that first sealing...he was tall and of a commanding figure, full of Life...Yes; I could tell you many things that I cannot write – I remember every word he...ever said to me of importance...”
And, heartbreakingly:
http://www.wivesofjosephsmith.org/05-Zi ... Jacobs.htm
In 1839, the Huntington family arrived in Nauvoo, along with daughter, Zina. Within months, Zina’s Mother died from the malaria epidemic which claimed the lives of many of the early Nauvoo settlers. About this same time, Zina met and was courted by Henry B. Jacobs, a handsome and talented musician. Sometime during Henry’s courtship of Zina, Joseph Smith explained to Zina the “principle of plural marriage” and asked her to become one of his wives. Zina remembers the conflict she felt about Joseph’s proposal, and her budding relationship with Henry: “O dear Heaven, grant me wisdom! Help me to know the way. O Lord, my god, let thy will be done and with thine arm around about to guide, shield and direct...” Zina declined Joseph’s proposal and chose to marry Henry. They were married on March 7, 1841.
Zina later wrote, that within months of her marriage to Henry, “[Joseph] sent word to me by my brother, saying, ‘Tell Zina, I put it off and put it off till an angel with a drawn sword stood by me and told me if I did not establish that principle upon the earth I would lose my position and my life’”. Joseph further explained that, “the Lord had made it known to him she was to be his celestial wife.”
Zina chose to obey this commandment and married Joseph on October 27. She later recalled, “When I heard that God had revealed the law of celestial marriag...I obtained a testimony for myself that God had required that order to be established in this church...I made a greater sacrifise than to give my life for I never anticipated again to be looked upon as an honerable woman by those I dearly loved...”. Zina continued, “It was something too sacred to be talked about; it was more to me than life or death. I never breathed it for years”.
Zina’s first husband, Henry, was aware of this wedding and they continued to live in the same home. He believed that “whatever the Prophet did was right, without making the wisdom of God’s authorities bend to the reasoning of any man.” Over the next few years, Henry was sent on several missions to Chicago, Western New York and Tennessee. Henry missed his family and wrote home often. One of Henry’s missionary companions, John D. Lee, said, “Jacobs was bragging about his wife and two children, what a true, virtuous, lovely woman she was. He almost worshiped her...”.
Shortly after Joseph Smith’s death in 1844, Zina married Brigham Young. In May of 1846, Henry was sent on a mission to England. In Henry’s absence, Zina began to live openly as Brigham’s wife and remained so throughout her life in Utah. Henry seemed to struggle with this arrangement and later wrote to Zina, “...the same affection is there...But I feel alone...I do not Blame Eny person...may the Lord our Father bless Brother Brigham...all is right according to the Law of the Celestial Kingdom of our God Joseph.”