Years ago I saw a reading over 300 nm on an analogue DME display on a B737-200. We had just departed Porto Santo after a fuel stop on the way to Tenerife, before the Madeira islands had any VOR or DME, so we tuned Tenerife North VORDME before takeoff. At about 5000 ft the DME came in, a good lock with ident, and we verified that the reading was about right from checking the airways charts. Obviously not line of sight - there must have been some ducting at work.
The ground station cannot "know" how far away the interrogating aircraft is - it just sends a response to the interrogation. The timing & range calculation are done on the aircraft, so surely any range limit would come from the aircraft kit?