It's simple, when constructing the RE lie, you make as few changes to reality in the hardest to notice ways. IE you shrink the oceans where no civilization exists.
Not the whole of the ocean as is suggested by quick photoshops of our map.
Take an example I think you guys might understand.
Your teacher hands you a map of the flat earth, scissors (with rounded tip) and some elmers glue.
Your assignment is to make a RE from a FE. She even gives you instructions.
1. Cut out the continents -Antarctica from the FE map.
2. Glue them onto the RE globe.
You'll notice the major changes are in the oceans between continents. Not between continents themselves or island groups. You'll notice the continents haven't shrunk. The distance from NZ to AU is exactly the same.
Now if I was rude and you are actually in 5th grade, you may notice that the flat continents did not glue so well onto the round map. There are adjustments that need to be made in order for flat continents to fit onto a round map. This is the exact reason why the RE'ers construct their round maps with many images, lots of editing, and usually cloud cover.