The original statement was "t
he ground return could damage the antenna" It appears many are talking about the actual radar tx/rx.
You will not damage the antenna unless mishandled or the radome hits something really hard

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Yes, modern radar tx/rx's are much less powerful as the rx's are indeed more sensitive.They are highly sophisticated and pretty much pilot and engineer proof in operation.
But many maintenance manuals do not allow operation whilst anywhere near a building / metal structures.Damage is unlikely but it is not allowed 'just in case' like many things in the industry. Such high frequencies are not good for people and should be avoided.
So your trainer is in essence incorrect.The WXR in general can be used (and are) on the ground given it is away from people, refueling and structures (distances differ so not quoted), ie lining up , throttles fwd etc.
It (the antenna) will not be damaged by ground returns.Their is a possibility of receiver damage if operated in close proximity to metal structures.There are electronic cct's that stop damage but why test it out unnecessarily?