Funny thing, Murray Carter teaches the coin trick. So does Chad Ward.
The width of the spine is not a big source of error with the coin trick. The coin trick assumes the bottom of the spine (on each side) and not the center, and always (by necessity) measures from the bottom face of the knife at the spine. Thus it measures the edge angle on each side of the knife without any error inherent from "guesstimating" the spine's center.
If you understand sharpening, you know the goal is not to create the desired angle perfectly, but to create an edge which is consistently close. The coin trick isn't a bad way to establishing a new edge angle on a knife at the heel. After sectioning the first stone-width though, it's a misleading distraction. And for returning to an established angle, it's not as good as "clicking in."
I don't like the coin trick myself, but there other things besides spine width making it problematic. Its highly dependent on placing the stack of coins and the knife in exactly the same position ever time, which is another way of saying you can only reproduce the desired angle from that one position. Get the spine a little off the edge or the center of the coin (whichever you've chosen), and you've shortened the base and hypotenuse, while decreasing the height. Furthermore, at ~0.07" width, a quarter isn't what you'd call a precise tool in finding a very specific angle within plus or minus 1*. Take those two together, and you can see what I mean about "misleading."
A stack of 7 quarters (typical stack size) has a way of falling over with very little provocation. So on top of its other shortcomings, the coin trick is a PITA.
More generally, I feel it's a mistake to try and pursue precise angles too ardently, since you'll never really achieve them; just as it's a mistake not to "do your best," to find and hold whatever is optimal for your knife.
It's attractive to a certain mind set though, that is one which prefers the security of apparently objective, external measurements, to measurements taken by touch (like clicking in) and by eye. At the end of the day, good freehand sharpening is going to depend almost entirely on how well you train your wrist and the techniques like the coin trick are mostly ways of getting started on that. Other ways, such as referring to large pictures of the desired angle, work just as well.
Done right, sharpening is a practical discipline acting as a handmaiden to something else, like cooking. It's neither an exact science nor an end in itself. The best you can do is bring some experience and perspective to the task.
Bottom line: Whatever works.
PS. You've said some very interesting things in the short time you've been on CT. Welcome!
Edited by boar_d_laze - 10/29/11 at 10:52pm