I doubt seriously that Brazil ATC (air traffic control) had radar coverage over the remote area of the jungle where the mid-air took place. That would make it like, say, the airspace over the North Atlantic Ocean.
RVSM is
Reduced Vertical Separation Minima and
TCAS is
Traffic Alert and Collision Avoidance System. The former is possible because of the later. RVSM reduces altitude separation between aircraft (generally flying in opposite directions, or head-on) to 1000-ft (used to be 2000-ft at altitudes above FL 280 - 28,000'). RVSM was first used on the North Atlantic air navigation tracks a few years ago.
TCAS-II allows aircraft to "see" each other on a variety of displays and issues warnings and conflict resolution advisories ("CLIMB .. CLIMB NOW") if the "Tau" (time-based) envelope of protection is violated.
TCAS-II is a function of the aircraft's Mode-S (data-link) transponder system. An aircraft without a Mode-S transponder (or with an inoperative Mode-S transponder) is invisible on the TCAS-II system and must not accept a clearance into a RVSM environment.
I flew the Beta version of the original Bendix TCAS-II system in the mid-1980s on a Boeing 737-200 and a North American Sabreliner 65. It worked beautifully then and they work much better now.
TCAS-I and TCAS-II have prevented innumerable mid-air collisions. In fact, it is almost inconceivable that two aircraft equipped with TCAS-II could ever collide in flight.
As an ALPA-trained airline accident investigator, I would put TCAS in the top five of all-time aviation safety innovations. This mid-air over the jungles of Brazil should never have happened with TCAS. Now we are beginning to learn why.
For more info see Wikipedia:
http://en.wikipedia.org/wiki/Traffic_Collision_Avoidance_SystemTCAS-II display on weather radar screen.