tubby , I do not know about the specifics of Airbus, but in many modern aircraft the ADC may use both pitot/static inputs.
In some cases, gross pressure differences will flag an ADC error or shut the system down. In other situations, those systems using the ADC output might average, or compare raw data or a combination of data from each ADC, and depending on the system logic, differing displays / warnings might be seen.
In the incident you cite, you may wish to investigate how the effected subsystems use the ADC output and what data type is required. This might isolate which ADC dominated and thus indicate which pitot system (if applicable) was at fault.
For some lateral thinking, you could investigate how the ADCs use TAT. IIRC temperature gets into all sorts of calculations and corrections (Mach etc) and thus a TAT fault might be the root of the indications. I suspect that TAT probe icing is more likely than pitot icing; also if Mach changes in the ADC (TAT trend toward zero), the EFIS IAS will also change.
The detailed in the articles above will explain why airframe icing would not have been present in these rare circumstances, and why very few returns are seen on WXR.
Re “…MD , No pitot icing problems…”
Except when the pitot heaters are not turned on; check for an accident quite some time ago on this subject.