Are snatch pickups used today?
No, although they were used up into the 1990s. Wikipedia has an article on this - called the Fulton Recovery system. Your quoted paragraph is incorrect - U.S. Air Force Special Operations Command (AFSOC) did use the system, on modified MC-130s. Despite the danger, Wikipedia only mentions one death using the system, though given the clandestine nature of many of the missions it was used on, it would not be surprising if there were other as yet unrecorded instances of its use.

Modern special operations helicopters have a much greater range, and some, like the MH-53, MH-47, and MH-60, are actually air-refuelable, extending their range. Additionally, the CV-22 Osprey has a much greater range and speed than a traditional helicopter. These improvements in extraction vehicles made the 'skyhook' system obsolete. 

Note that this article mentions the British used the system in 2001 to rescue an injured soldier behind enemy lines.