<font face="Verdana, Arial, Helvetica" size="2">Was there/is there a problem with Airbus aircraft that would indicate this is unique to the A330/340?</font>
You can debate that one till the cows come home. The A340 went into "AoA protection law" because the AoA reached the 'alpha prot' threshold value in the turbulence. Thus it then held the 'alpha prot' value of AoA until a nose-down sidestick input was made some 28 seconds after the incident began.
It could be argued that the crew should have made a nose-down sidestick input much earlier, but that's easy to say with the benefit of hindsight. It could perhaps be argued that the "AoA protection law" is of limited value in the cruise at FL360.