_Every_ map projection distorts reality in some way. There's simply no way to accurately portray a sphere as a two dimensional object without some trade-offs. The Mercator projection has some useful trade offs, which is why Google maps used it for so long (and still does as certain scales, I believe).

I don't believe the authagraph projection is even the best map projection for preserving things like shape and area (other projections such as the Cahill–Keyes projection or Dymaxion projection seem better for both).

But of course, if you want the least amount of distortion, just get a globe.

If you cut meat with an ax, this is a mistake, but it isn't the ax which is mistaken.