JOEL - The wearing of a beard has sometimes been associated with the perception that a person is covering his face because he has has something to hide. I suppose that is partly why missionaries are asked not to have them now. They don't want to give anyone the slightest possible impression that they are hiding something and they want to be assured of the clean-cut look. A few decades ago I believe men were asked to shave off their beards before they could go to the temple.
According to Bishop Victor L. Brown in April 1977:
"President Lee on several occasions gave wise counsel with respect to following the living prophet." President Brown then quotes President Harold B. Lee's story of a woman who wrote,
"Tomorrow my husband will shave off his long, full beard. Because of the request of the stake president and your direction in the Priesthood Bulletin, he must not have the appearance of evil or rebellion if he is to get a recommend to go to the temple." Then President Lee responded to the letter,
"Now, in your letter you tell me that you are saddened because with the shaving off of the beard and the cutting of the hair, which, to you, made your husband appear as the prophets Moses and Jacob, he would no longer bear that resemblance. I wonder if you might not be wiser to think of following the appearance of the prophets of today. President David O. McKay had no beard or long hair; neither did President Joseph Fielding Smith; and neither does your humble servant whom you have acknowledged as the Lord's prophet.
Why is it that you want your husband to look like Moses and Jacob, rather than to look like the modern prophets to whom you are expressing allegiance? "
Here's something Elder Marvin J. Ashton said in October 1976:
"Generally the cover or jacket of a book is designed to sell what is inside. We will not have to die to be judged by the cover of the book of life. To those who would say, "It's what you really are inside that counts, not the length of the hair or beard," I would say, "If this is true, and I agree it is, why run the risk of looking like something you're not?"
This is all I could find on anything that church leaders have said about it.
Of course these quotes were 25 years ago. I do not know of any such restrictions now. In fact, a counselor in my own ward bishopric sports a gotee and looks really good in it. And he goes to the temple quite often.
I believe a lot of it has to do with how the general public perceives a person who is wearing a beard at a given time or in a specific culture. In some peoples minds the gotee reminds them of evil because paintings of Satan have often shown him sporting a gotee. Also, it has often been used as an identifier of the bad guy in movies and TV shows.
Personally, I see nothing wrong with wearing a beard. However, it may take a little longer for a few people to get past the first impression and see the man for who he really is; as in the case with the man you are refering to. He probably should not let the beard get too long though, when you consider the following scripture:
"And I went out after him, and smote him, and delivered [it] out of his mouth: and when he arose against me, I caught [him] by his beard, and smote him, and slew him." (1 Samuel 17:35)