This has been said over and over again in the last 48 hours.
These are distances people are traveling on a regular basis. Hundreds of thousands of people every day. Tarmac was laid, train lines were laid. If the distances were three times what is being reported, surely someone would have noticed. Before children I did a fair bit of traveling and have traveled some of these distances myself. There are no calculations involved. It is measurement.
Say "authority" says that the distance between two cities is 100km and it is really 300km, do you really think things would not fall apart quickly as the new train line was 200km of track too short, as people ran out of petrol, as people planned to take an hour to drive it and found it 3 hours. What about these undiscovered lands between? It is completely unfeasible that we are being lied to about distances between cities.
Which takes me back to what I said about constructing a model. Take a roughly southern ring around the earth and the cities between them, so say Sydney, Perth, Wellington, Cape Town, Rio, and a few of the smaller islands in between. Use the tried and tested distances and join them together in a scale model. You end up with a ring model on your table.
Now do the same for equatorial cities and land marks. You get a larger ring. Repeat one last time for something a bit more northern, say London, Antwerp, Warsaw, etc. You get another smaller ring. Three rings, small, large, small. Now consider that Libya is north of Cape Town, Warsaw is north of Lybia, the only way to start joining these three rings in a model is to make it 3 dimensional and it starts to look a bit like a globe.
Doing the northern ring with London on a flat earth works. Doing an equatorial ring and joining it to the northern ring you made, just about works and is still flat. Some of the distances are a bit off to make it flat, but we are talking about bluetac and straws models here. But try to add anything south of the equator and it all breaks down. That is because the earth is not flat and simple geography points to that.
If you do not accept that, give us a scale map that says otherwise and actually works.