Good question, and you guessed correctly.
The planes to which you refer comprise the "Janet fleet" - a small fleet of passenger aircraft established back in 1972 that are operated for the U.S. Air Force by a private company called EG&G and are used to transport military and contractor employees. They operate out of their own -- heavily guarded -- private terminal at McCarran and primarily serve the Nevada National Security Site (previously the Nevada Test site, which was formerly known as the Nevada Proving Ground) and Area 51. Hundreds of workers board the flights each day.
Apparently, no one (at least no one who's telling) knows the origin of the term "Janet" and whether it's an official name, code word, or acronym.
Currently, the Janet fleet consists of six Boeing 737-600s painted white with a prominent red cheatline, as you describe. There are also two Beechcraft 1900s and three Beechcraft 200Cs painted white with less prominent blue trim stripes.
All the 737-600 aircraft are ex-Air China, we understand, and in the main were operated by the now defunct China Southwest Airlines in 2008.
