Section 89 of the Doctrine & Covenants (D&C), also known as the Word of Wisdom, is a revelation appertaining to the health and strength of our physical bodies. The focus relative to this question is 'hot drinks' and caffeine, two separate items which, when lumped together as one, result in misconceptions concerning the Word of Wisdom.
And again, hot drinks are not for the body or belly. (D&C 89:9)
As noted in the question, the confusion occurs when one misunderstands the Word of Wisdom. Some members of the Church as well as many non-members understand the Word of Wisdom, specifically the definition of 'hot drinks' mentioned in verse nine, this way:
Hot drinks = coffee and tea. Coffee and tea have relatively high levels of caffeine, therefore the reason LDS abstain from coffee and tea is because of the caffeine, therefore LDS abstain from all products containing caffeine, true?
False, actually. This presents a logical error, known as a fallacy of definition, because the definition is too broad. The official and correct definition of 'hot drinks' as found in the Word of Wisdom is simply this:
Hot drinks = coffee and tea.
The Word of Wisdom is a basic law of health, in other words, it is a good starting point. Add to this the "body is a temple" scripture found in the Bible and we begin to have a clearer understanding of the Church's emphasis on being vigilant of what we ingest and on the well being of our bodies. The standard works have many scriptures admonishing us not to defile the mind or the body. "The promises associated with the Word of Wisdom are considered both temporal and spiritual. The temporal promise has been interpreted as better health, and the spiritual promise as a closer relationship to God."
Latter-day Saints, with the Word of Wisdom as a foundation and mindful of both the scriptures and the counsel of a living prophet, are encouraged to personalize their health regimen and-just like anyone else who chooses to live a healthy lifestyle-quickly realize that there are many paths and options. At this juncture, members of the Church decide for themselves if they will follow the basic parameters of the Word of Wisdom (that is, to simply abstain from coffee, tea, alcohol and tobacco), or if they will go the extra mile, for example by not drinking any caffeinated drinks or eating any caffeinated products whatsoever. In the Church, we refer to this as living according to what the Holy Spirit has revealed to each of us, or in this instance, living according to the spirit of the Word of Wisdom.
The Word of Wisdom contains two kinds of instructions: (1) prohibitions, and (2) counsel. The prohibitions are binding upon the Saints; the counsel, precisely because it is counsel, is up to each of us as individuals. The prohibition in question is against 'hot drinks.' The Church has, as a body, accepted that the hot drinks in question are coffee and tea. The high caffeine content of these drinks has been widely discussed, and is generally accepted, as a likely explanation for the prohibition; but this explanation has, of itself, no binding doctrinal force.
A personalized interpretation of the Word of Wisdom oftentimes adds to the confusion of "what is the Word of Wisdom." Our personal interpretation should not be forced on other members, nor should it be promoted as THE Word of Wisdom. It isn't THE Word of Wisdom; it is YOUR personalized version that you view as consonant with the spirit of the Word of Wisdom. Keeping this in mind, when someone informs us that "THE Word of Wisdom says don't drink caffeinated beverages," he/she is incorrect.
"But," some may ask, "what about what President Hinckley said on the 'Larry King Show' and '60 Minutes'?" President Hinckley's acknowledgement of his interviewer's leading questions is not indicative of a shift in formal Church policy. It doesn't work that way. If the President of the Church ever wants to formally include caffeine in the Word of Wisdom, he will do so through established Church channels, not by a media interview.