Not so. The article is not exaggerating anything here, if you read it carefully. As another user pointed out, an isolated cell will conform to a circle. The crucial point here is that there is a 3-way junction between the cells that pulls equally in all 3 directions. And it makes sense if you think about it as well. 360 degrees (all directions) divided equally into 3 (surface tensions pulling equally in 3 directions) you get 120 degrees. Which is also, you guessed it, the interior angle of each vertex of a hexagon!

The example with the bundle of straws works on a similar concept, except instead of pulling, you are applying a force to the perimeter of a circle from 6 different directions. 360/6 = 60 degrees, the central angle made by dividing the perimeter into 6 straight sections (I. E. a hexagon).