As far as I know, nobody said that the crew didn’t read back and didn’t accept the clearance properly, and everybody said that they were indeed cleared to FL 370. As far as I know NTSB/CENIPA blames the crew (besides transponder issue) for “Before beginning a flight, the pilot-in-command of an aircraft shall familiarize himself with all available information appropriate to the intended operation.” and they didn’t. And “The Legacy crew failed to act with special caution, considering that the pilots had little knowledge, not only of the Legacy’s operation, but of Brazilian air space:
• when they did not question the authorization received, with level FL370 (37,000 feet) for the entire route, differently than in the original flight plan, which foresaw different levels than previously authorized;
• when they perceived, by the onboard documentation (and, if they did not perceive, they had the professional duty to have done so) that level FL370 (37,000 feet) on airway UZ6 provided for traffic in the direction opposite that in which the aircraft was proceeding.”