"Regardless of whether the distiller is making whiskey, brandy, tequila, rum or vodka, what comes off the still is not sweet." After distillation there is NO SUGAR is left in the product that leaves the still. Just because rum is made from a derivative of the sugarcane plant that provides the majority of the sugar to the world, doesn't mean that the rum has sugar in it. I've never heard people tell me that brandy or cognac is sugary, a spirit made from the juices of grapes or even tequila made from agave the source of one of the sweetest nectars available."
Here is where the misconception is coming from. Many of the producers of rum will take the spirit upwards of 96% alcohol during the distillation process. When the distillate reaches this level of alcohol it is what is called a "Neutral Spirit" or Vodka. Vodka can be made from any plant whose sugars can be turned into alcohol with enzymes, including sugarcane. You hear that the better vodkas have been 5 to 10 times distilled. All this means is that they have had to distill it that many times to reach the 96% or so to reach the neutral spirit level.
When your alcohol is this pure, it takes a lot of time in a barrel to mellow the spirit and they tend to be very dry in flavor. For many producers, rather than letting their products age would rather add flavors, spices and yes sugar to simulate a properly aged and blended rum. These are the products that have given rum it's sugar sweet reputation.
Good rum is a blend of pot distilled and column distilled rums that have been on an average distilled to 63% alcohol with only the hearts of the run being utilized for the final products. After they are blended they are placed in barrels of many origins where they spend sufficient time to smooth and develop the flavor of the expression without the addition of sugars, glycerines or flavorings to achieve the flavor. Rum is a fabulous spirit that unfortunately has been allowed to run unchecked throughout the world for too long and as a result the consumer can't tell the real rum from the contrived. A simple matter of labeling would solve most of the problem, I have no problem with the people that make these artificially flavored rums, it just needs to be labeled like all other food showing the ingredients added to the distillate in production.