So you cite the low fat craze but then suggest going to equal extremes in basically cutting out all sugar, even if it's in otherwise nutritious food? Give it a decade or two and Americans will be fatter and less healthy and blaming their no-sugar diets. Already plenty of problems with the related low-carb diet craze that followed the low-fat craze.
Common sense: cut out foods with no nutritional value, replace with healthier foods and not eating/drinking so damn much, and exercise. Or get caught up in the latest scare tactic some guy used to create a bestselling book and/or a bunch of overpriced diet food and drink. Worried about sugar: WATER DOWN your drink (a point you still ignore) or drink it with meals - it turns out fruit fiber isn't the only thing that you can eat to slow down sugar processing.
I've never heard anyone credible suggest that you shouldn't drink any fruit juice. Most suggest drinking pure fruit juice (without added sugar), drinking a cup or two a day, etc. If you're really that worried about sugar, you drink water or unsweetened tea, not coconut water.
Here ya go, have at it:
http://advances.nutrition.org/content/6/2/236S.full
https://www.hsph.harvard.edu/nutritionsource/healthy-drinks/drinks-to-consume-in-moderation/
A pretty balanced look at both sides of the argument that mentions the idea of blending fruit into your drink to preserve the fiber:
http://www.foodandnutrition.org/May-June-2015/Is-Fruit-Juice-Just-Another-Sugary-Drink/
http://www.medicaldaily.com/fruit-j...healthy-juices-you-can-feel-good-about-306648
http://www.eatright.org/resource/homefoodsafety/safety-tips/food/the-juicing-trend-about-raw-juice
And pretty much every article with the alarming "fruit juice as bad as cyanide-laced cigarettes?"-type headline has moderation advice that reads exactly like what I said.
I did enough work - you can go call those physicians, pediatricians and nutritionists on your own.