I believe you have missed the corporate-wage-slave ’s comment completely. Same Day Change (for free) is only available on BA’s short-haul network. In addition to this, you must be holding a BA issued Economy Plus or ,Club Europe fare to benefit. On top of this, the itinerary must be “simple”/point-to-point, it cannot be a connecting itinerary.

In your scenario, you would never received a free same day change unless you had a flexible fare with no change fee and by random chance there was absolutely no fare difference between your original ticket and the current price for the proposed change flight. Sometimes in cases of disruption or overbooking, you may get lucky at the airport by asking but it certainly isn’t to be expected.