Red eye has nothing to do with the position of the flash.
Absolutely wrong. it has EVERYTHING to do with the position
as Wikipedia says right off the top:
The red-eye effect in photography is the common appearance of red pupils in color photographs of eyes. It occurs when using a photographic flash very close to the camera lens (as with most compact cameras), in ambient low light.
I shoot a DSLR (Canon 50D) with an external flash and even with the flash head square to the subject, I never have red eye because the flash is 8-12" above the lens' axis. Even the built-in pop-up flash is high enough to be off-axis from the lens. Compare that to the typical P&S camera's lens-flash relationship.
The rest of your post is correct, though. "Red-eye reduction" is done by flashing light to constrict the pupil and this reduce the aperture where light can bounce against the retina and back. Since moving the flash away from the lens is impossible in tiny bodies, blinking the strobe is the annoying workaround.
As for the EVO, because the phone/camera is likely to be held vertically (portrait), one of the LEDs can't be placed at the "bottom", but there's no reason they could park the LEDs in the corners - making a triangle with the lens at the apex - other than it's a more costly and cumbersome solution. As the ifixit.com teardown shows, the flash LEDs are on a common board.