A friend once told me that even ignoring the size of the scoops, a "spindown" D20 (Where neighboring faces are numbered sequentially, for easy look-ups.) produces different odds than a normal D20, which has more varied neighboring faces. Is this true?
In theory: No; each side of a perfect n-sided die has a 1 in n chance of appearing.
In the real world: Yes; die shapes are imperfect, often favoring opposing sides, hence the tradition of making sure opposing sides are equal on average. As explained in this answer. Having all high numbers on one side also makes it more easy to fake fair rolls, like merely spinning or skittering the die.