The article doesn't say that - it says that glucose and fructose are handled differently (which is true; both occur from natural and processed sources) and that naturally-occurring sugars often come in high-fiber foods, and fiber impacts sugar uptake (which is also true). Sucrose is sucrose, whether naturally occurring or from processed sources.
The issue with "processed sugars" is that they appear in forms which cause you to not necessarily get enough fiber with them, and in form factors that are very easy to overconsume, but biochemically, 19g of table sugar and a couple of Benefiber caps are going to do approximately the same thing as an apple. Being processed doesn't make it magically toxic.