For me, they were on a given sector frequency, and the boundary of that sector was until close to the point they collided, and they had no reason to select another one.
The following affirmative was published by Folha (biggest Brazillian newspaper) and all Brazilian newspapers as an extract of NTSB/CENIPA final report (It's not my words, it's not my opinion. Don't kill the messenger!):
"The most relevant neglect conduct of the North American pilots is in respect to radio communication. They say neither they nor any other pilot in any part of the world needs controllers to know at what frequencies they should position their communications apparatus . The navigation charts register the frequencies sector by sector. Lepore and Paladino knew that in Sector 9, between São José and Brasilia, the frequencies are 125.05MHz 133.10MHz and 121.50MHz. On entering Sector 7, in Brasilia to Manaus, the frequencies are 123.30MHz, 128.00MHz, 133.05MHz, 135 90MHz and 121.50MHz. The frequency 121.50MHz appears in all of the sectors because it is the universal emergency band."
The collision occurred in Sector 7 shortly before entry into FIR Amazônica.
The clearance from ATC is the final instruction on what to do and if they fcuked it up and didnt catch it on the read-back from the pilots then it is ATC who are at fault.
This is not in dispute by anyone. That is why controllers were indicted and besides that, for "lack of diligence".