If it were an F1 with its VCU, I'd say definitely get the tyres matching on make and model. I'm not so sure with the F2 and its Haldex - but if the garage says that the Haldex is OK and the diff damage was caused by "the 4x4 kicking in" you have to question something. The system is designed for the 4x4 to 'kick in' - that's exactly what it is there for
So something isn't adding up right, especially on a 2011 car with the stronger diff.
This is a perfect thread for showing how mismatching tyres can throw the transmission on a F1, and these on the face of it looked like the same tyre from the same manufacturer...
https://www.landyzone.co.uk/land-rover/feels-like-driving-with-brakes-on.260939/
Hope they replaced the diff with a decent one, not one off a < 2010 car they found at a breakers!