"Thou shalt not plant thee a grove of any trees near unto the altar of the Lord thy God"it rained before the flood.
I do not know of anyone yet who has used Deuteronomy 16:21 to argue that there should be no trees on temple (or church) grounds. But if we were to read that verse literally we may come to the conclusion that we should not plant trees anywhere near the temple. There may even be squabbles about how many trees are allowed (because one or two trees is not a grove so that may be OK). But it would not make any difference since the whole argument rests on a misunderstanding of the actual text of that verse.
The problem is there is one word in that verse which the KJV renders as "grove" but in reality is much more complex. Let us use another translation to illuminate the true meaning of that verse. The New International Version renders it as:
"Do not set up any wooden Asherah pole beside the altar you build to the LORD your God"When the KJV translators were doing their work they had no idea what the word "אֲשֵׁרָה" meant, but from the context it seemed to refer to a grove of trees. So they translated it as "grove" and left it at that. It was not until hundreds of years later that Biblical scholars learned that "אֲשֵׁרָה" is the name of a Middle Eastern female deity commonly worshiped at the time the Bible was being written. Thus more modern translations (and a footnote in the LDS version of the KJV) translate "אֲשֵׁרָה" as Asherah and note the background and context.
Because we have easy access to the history surrounding Asherah we can avoid some of the possible misinterpretations of verses such as Deuteronomy 16:21, which is why we don't have people suggesting that the trees around the temple should be cut down. But if we had no other information about Asherah and all we had to go on was the KJV translation then it would be possible for us to misunderstand that verse and use it as justification for cutting down the trees on temple grounds. This potential misunderstanding is easily resolved but there are others in the scriptures that are not so obvious.
For example the phrase "his hand is stretched out still" which appears several times in Isaiah is sometimes used as a comforting phrase to show the love and mercy of God. But if we consider the phrase in context we quickly see that it does not refer to a merciful, "extended helping hand" but rather to a fist ready to smite in anger. That misunderstanding is rather benign since it won't lead us to go about chopping down trees. At most it will make us think about being kind to others so it's not really a big deal.
But there are other more subtle misunderstandings of scriptural passages which over the years have come to supplant the original meaning. And sometimes ideas that do not come from scripture work their way into our thinking and we mistake them for doctrine even when the scriptures say the exact opposite. That is why it is advantageous to study the scriptures in the context they were written as much as possible. This approach will help us see and understand any misconceptions we may have that we never knew we had.