A310 driver
You read my post too fast I think , look again : I did not say that ATC and ACAS were " primary" means of separation, but " main" means. Because I agree with you, in IFR , the primary means of anti-collision is ATC, and ACAS is the ultimate last minute one. (In between there is visual aquisition) .
The rest of your post is fully correct, except that the communication problems were not between adjacent sectors, ( i.e sectors within a same unit, seing teh same radar picure ) but adjacent centres , i.e 3 different ATC units located hunderds of miles appart and using diferent ATC systems and radars.
From what it transpires now, Manaus expected the legacy a 360 and since they never saw it coming as the Xponder was not on, and it did not call already , they had little reason to " move" the 737 out of the airway . What happened in Campos and Brasilia is less clear.The transcript of the coordination between the two will probably shed some light when we see it.
The Brasilia ATC system showed the legacy at 360 ( while it was in fact at 370) that we know, and we know why.
I do not think Brasilia had the 737 on radar nor on R/T contact. Again the radar recording of Brasilia will show this when it will become public.
( and check your PM)