The Brazilian non-pilot position I think is slightly different.
to paraphrase their position:
1 - In Brazil the rules/expectation are that the flight will move to its flight planned altitude without communicating with ATC - contrary to what everyone else in the world seems to do.
2 - ATC are so ingrained in this expectation that even though the flight checks in at FL370 with a planned descent in the next few minutes, ATC wouldn't mention the expected descent while confirming current cleared level.
3 - ATC wouldn't look (or would expect a 'casual' descent) so the fact that 7 minutes after Brasilia the plane is still showing level at FL370 wouldn't cause ATC to contact the plane or to note anything on their strip.
4 - Compliance with this expectation is such that it is reasonable for the computer to updated the display of planned/(cleared?) level without any controller action or data from the transponder
While this may look like an absurd interpretation of how flights operate in real life (from my North American and European perspective) it might be possible that Brazil operates way outside ICAO norms in terms of ATC/Pilot interaction
If so this would clearly be a big factor. If its just a bo**cks view of the non-professional, it just brings us back to the question of what was going on in the ATC processes that let this happen.