These are a couple of "old wive's tales". They have been repeated so much that we believe them without thinking about them. Modern fly fishing books have corrected the error, although the Mustad site continues to say that the hook eye position matters on angle of set. It does not.

The position of the hook eye has no relationship to the angle of the hook set. The hook set is performed with the fish's mouth closed on the hook and the angle of the set is the angle of pull between the rod tip and the hook eye. So it is the rod position that determines the angle of the hook set.

For example, one would think that a down eye hook would cause the angle of pull to be "down" on the hook, but the angle of pull is actually up if the rod tip is above the level of the hook when the hook set occurs. Once the hook point penetrates flesh, the hook pulls on the flesh deforming it and simultaneously the hook rotates in line with the angle of pull of the line.

The hook gape is the distance between the hook point and the hook shank. It is unaffected by the hook eye angle. What narrows the hook gape is the material that is tied on the fly opposite the hook point. The distance between the hook eye and hook point can vary with the eye position BUT is unimportant unless the hook is very short.

I think hook eye postion is more about the aesthetics of the fly and the ease of tying the fly than any effectiveness in hooking.