Just for the record:
The towing fitting on an A340-500/600 is a larger diameter than A340-200/300 or A330-200/300. The NLG tyres are the same size albeit a higher ply rating.
The reason for the incompatibility is to prevent an A345/6 towbar from being used on the A330/A340-200/300 aircraft. The axial and radial shear pins on the A345/6 are stronger to account for the heavier weights. If an A345/6 towbar was used on an A330/A340-200/300 the shear pins would not shear at a low enough load to prevent damage to the NLG.
I think the reason for the diversion will raise a few eyebrows when Airbus issue the OIT/FOT.