It doesn't sound like this crew corrected the problem by just 'pushing two buttons'
The report said they had to 'turn off two computers' i've only flown Boeing and Douglas products but It sounds to me like they were pulling circuit breakers to disable these 'protections'
The Airbus attitude of 'we always know better than the pilot' has proven to be a major problem.
There should be just one switch you can operate to disable all 'flight control filtering' and go to direct law, just as is the case on the B777 and B787.