No, I was unaware of any South Park episode on the Mormons, so can't comment.
I don't know which Mormon community you are talking about, but my instincts tell me it was probably in Utah, or maybe Idaho. The woman you are talking about was most likely one who was born into the faith, and surrounded by a majority Mormon population, and also most likely multi-generational Mormon. Individuals like these often live a pretty sheltered life, and get spoon-fed almost everything they know, as opposed to studying on your own initiative to find out what you should know.
Regarding the Bible, Mormons "believe the Bible to be the Word of God insofar as it is translated correctly". The King James Version is the one they accept most, as they believe it is the most accurate translation out there. (That is why that LDS woman probably thought the Bible was written in the King's English, because that's probably the only Bible she has ever seen. Probably no-one ever told her about all the other translations or versions of the Bible, and how it was written in Hebrew and Greek, etc.)
Mormonism teaches that the Church of Jesus Christ has a living Prophet who continues to receive new Revelations from God. During the time of the Old Testament, the Nation of Israel had living Prophets who received revelations; and at the time of the Apostles revelations continued to be received. Many new revelations were revealed along the way. Protestants teach that the last revelation has been given, and all the needed Revelations have been recorded in the Bible, and so there is no longer any need for living Prophets or New Revelations. In other words, the Heavens are sealed. Mormons see this as illogical and inconsistent with the way God deals with His people at any age. He has always revealed His Will thru a Prophet in the past, and there is nothing to say or prove that He is any different today.
For this reason, those born into Mormonism and live all their lives in a majority Mormon populated community feel they are simply following the ways of Old, listening to the message of God's Chosen Prophet, which is no different to them than you and I studying the Bible containing God's Revelations to understand God's will.
The whole problem with all this, as I see it, is that it all depends whether the Prophet at the head of the Mormon Church is a true Prophet of God, or not. The question behind that one is, Is the Mormon Church the True Church? and does what it teach constitute the Truth from God? How are we to know for sure? If you use the "Bible only" as the measuring rod for judging whether Mormonism is true or not, then there will follow a huge debate, because Mormon scholars have some pretty interesting arguments and interpretations of what is supposedly contained within the pages of the Bible. At B.Y.U. they offer courses in Religion, and Biblical studies, and they do get into studies of Hebrew and Greek and ancient languages and manuscripts, etc. etc. It might surprise you how well their arguments can hold up against conventional Protestant and Catholic interpretations of the Bible. (I know this, because I spent over 9 years studying it from a Mormon perspective.) But the question of Mormonism is even more complicated than this, for the reason that they have additional "Scriptures" which they consider to be on a par with the Bible (for example, the Book of Mormon, the Doctrine & Covenants and the Pearl of Great Price). Without getting into long dissertations on those, suffice it to say that Mormons consider these to be inspired of God and containing important revelations that are not found in the Bible, or else clarify a number of ambiguous teachings that are in the Bible, or that have been lost or distorted because of problems of translation.
Anyway, I am not trying to act as a Mormon apologist here, but rather just trying to explain how and why they are the way they are, so that you can understand better what is going on as you see these people in their day to day lives.
Anyway, as for the lady who did not know her Bible, I can assure you this is not typical of Mormons at large. Many of them know their Bibles by virtue of them being converted to Mormonism from other religions. Some from inside the Church have become ardent Biblical scholars, and can hold their own against scholars outside the Church. Every year, thousands of Church members go on a mission for two years somewhere in the world, and these people become pretty trained in the Bible, since they have to talk to people of other faiths and must know where these other people are coming from when dealing with religion and matters of faith and the scriptures.