I think he was implying not big in the ordinary sense but a freak, some sort of 3-headed monster if you will. JMO! Giants wouldn't have been considered natural by Smith or his contemporaries, I suspect.
You don't even need to go to a site that refutes Mormon claims. Here it is on the Church's own Missionary website (comeuntochrist.org, formerly mormon.org): "Like many Christians, we believe in God the Father, His Son Jesus Christ, and the Holy Spirit. However, Church members don’t believe in the traditional concept of the Trinity. We believe that the Father, the Son, and the Holy Ghost are three separate beings, united in purpose." emphasis added (https://www.churchofjesuschrist.org...church-of-jesus-christ-believe-in-the-trinity) Aside from the obvious heresy, this seems at first glance rather innocuous, right? But, think about it in the context of Matthew 1: 19-20: "19 Then Joseph her husband, being a just man, and not willing to make her a publick example, was minded to put her away privily. 20 But while he thought on these things, behold, the angel of the Lord appeared unto him in a dream, saying, Joseph, thou son of David, fear not to take unto thee Mary thy wife: for that which is conceived in her is of the Holy Ghost." Or Luke 1: 34-35: "34 Then said Mary unto the angel, How shall this be, seeing I know not a man? 35 And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God." Please forgive my use of the KJV of the Bible, it's the canonical scripture of the LDS Church. Now, I'm by no means an expert on scripture, but read in the context of the LDS concept of "The Godhead" (a.k.a. Trinity), what the angels are telling Mary and Joseph is a little odd. If read literally, that would mean the Holy Ghost is the father of Jesus on the Earth, NOT God. Do Mormons actually think this? I don't know. I DO know that I don't, and that this is one point among many that I have issues with.
No need to apologize for citing the KJV, I do it all the time. You make a very interesting point. If they were three separate beings, and if the Holy Spirit were the being that 'fathered' Jesus, then the Father would not be His 'father' (which contradicts 1 John 4:9 and other verses which tell us that the Son is God the Father's "only begotten"). It's one more contradiction to add to the heap of nonsense they concocted.