why, oh, why..
Let me have a go at question why:
First, lets bring into picture drag vs. speed curve.
It looks like a bowl, with a round bottom. That's the key.
As was reiterated here multiple times, best endurance is where the graph reaches its lowest point: least power is needed to counter the drag, so the fuel flow will be the lowest, and the tank will last the longest.
We gonna get some decent range at this speed, too.
However, if we increase the speed a tad, you'll notice that the drag will hardly change, since the curve's bottom is smooth and near its best drag point it actually has a flat slope. So increasing speed by 1% will pretty much get you almost 1% rise in range. The actual number will depend on the aircraft of course, but the key is: to find the max range speed you gotta go hunting to the right of the curve.
Is this along the lines of an explanation/proof that speaks to you?