They are probably also measuring by bird distance...
The actual phrase should be "as the crow flies." If you say "bird distance," you might get confused looks from people.
Just trying to help. :-)
That said, "bird distance" is going in my lexicon.
You may then proceed to explain this refers to the distance by camel.
You: Except on a globe, it is a great circle.
Me: 'Nobody said on the surface. I'm tunneling through.'