Glueball,
When Brasilia lost transponder signal, 1 hour before collision, and this was displayed at their ATC screen, they immediately should have called Legacy, ... and they didn’t. 30 before collision, when Brasilia lost radio communications, they should adopt all applicable procedures (bridge between planes, using emergency frequency, …), ... and they didn’t. After failing all of these procedures, they should put away all traffic against the Legacy because they didn’t know its altitude due to the transponder failure, ... and they didn’t. All errors after Brasilia, besides the transponder issue, are controllers procedures errors.
The accident was in a ACC-Brasilia sector, and Gol flight was already under control of ACC-Brasilia, and in ATC mind, Legacy were in FL 360, ATC didn’t guess that Legacy was FL 370. That it is why they didn’t guess that there was a mid-air collision risk at that moment. They assumed that it was just a transponder mistaken code issue.