Sounds a lot like a problem in the "control laws". Basically, there's a computer program the limits the fly-by-wire inputs throughtout the flight envelope.
Airbus has had "control law" issues before (and IIRC) they always finger the pilots first, claiming the programming is flawless. So that part is no suprise.
I can tell you a story of the dark and stormy night I was F/E on a functional check flight on a 727 after phase maintenance. This all happened so fast that it takes way longer to read it than it did to happen. It happened so fast, we were all pretty much stunned into inaction.
The Captain was an ex-Navy guy with a reputation for being a bit agressive. One of the checks was to turn off both yaw dampers, induce mild dutch roll (10-20 degree oscillation) and then turn on one yaw damper. The yaw damper should/did immediately stop the dutch roll. Repeat test for other yaw damper.
Well, F/O flew the first dutch roll (all you had to do to induce it was turn off the yaw dampers and push in some rudder and quickly release it. It would start dutch rolling with ever increasing amplitude. You just turned on the yaw damper when it was banking back an forth at about 20 degrees) and the Captain decided the F/O hadn't REALLY given it a good dutch roll.
So, the Captain does the next one. He pretty much pegs the rudder to the floor for a hearty second or so, which gets us rolling up to about 30 degrees or so and then he releases it all at once and lets the amplitude increase up to about 60-70 degrees in a heartbeat.
The cockpit is vewy, vewy, quiet. I'm hanging on to the F/O Desk, the maintenance guys are grabbing anything bolted to the floor.. and then the Captain reaches to slap on the yaw damper at about 70 degrees of bank and swinging for more. The maintenance chief yells "NO!"
WHAM! The yaw damper rolls us out right now.
The maintenance chief then debriefs the Captain for an extremely long time and in great detail about how the vert stab is attached to the aircraft and just what sort of stresses it can and cannot take. He describes in great detail just exactly how much he figures the T-tail got twisted and how he expects to have to do a two-day inspection on the airplane now.
We actually finished the rest of the check and rtb'd safely. They did re-check the vert stab but it was apparently OK.
I was always watching pretty close and spoke up readily when I flew with that guy after that though.