You can read the statements of the witnesses in the Introduction to the Book of Mormon. Neither group of witnesses mentions a cloth covering:
. . . And we declare with words of soberness, that an angel of God came down from heaven, and he brought and laid before our eyes, that we beheld and saw the plates and the engravings thereon; and we know that it is by the grace of God the Father, and our Lord Jesus Christ, that we beheld and bear record that these things are true. . . . (The Testimony of the Three Witnesses)
. . . Joseph Smith, the translator of this work, has shown unto us the plates of which hath been spoken, which have the appearance of gold; and as many of the leaves as the said Smith has translated we did handle with our hands; and we also saw the engravings thereon, all of which has the appearance of ancient work, and of curious workmanship. . . . (The Testimony of the Eight Witnesses)
Thus, the witnesses saw the plates and some handled them.
Sorry, a little too juvenile of a story for me to buy. . . .
Suit yourself.
Sorry - as with corrupting Masonic practices to create temple rituals, Smith also attempted to corrupt the KJV Bible in his strange book called "the Book of Mormon."