Are all world maps incorrectly dimensioned?

The world maps were probably not deliberately "falsified". There was an understandable reason for the reliable navigation.

By the way, there is a scene with "The true size of ..." from 2:42 min in the video. The link to directly test the true size of countries can be found on the right. Drag Germany onto the equator yourself.

But it's best to trust our globes to get the right proportions of land and water masses.

"The true size of ..." gives you a good feeling for the true proportions. Just click on the button and try it out.