'2-Headed' Coins DO NOT come from the U.S. mint.

Why is it impossible for the 2-headed coin to come from the U.S. mint?

The U.S. Mint (and most other world mints) have built-in protections against accidentally making coins that have the improper die rotation or die setup. The shaft of the dies are made to be a certain size and shape, so that they will only fit into the coin presses a certain way. Dies that have the obverse (heads) design on them have shafts of one shape, while the dies with the reverse (tails) design have a different shaped shaft. This prevents the mint workers from accidently making two-headed (or two-tailed) coins.

The way fake two-headed and two-tailed coins are made isn't what you'd expect, which is why many people who find them are reluctant to accept the truth about them. They are not made by cutting two coins in half and then sticking the halves together, which is why you won't see a seam along the edge giving the coin away. Instead, two-headed coins are made by hollowing out the center of one coin, leaving the reeded edge and heads side intact, and then shaving down a second coin so that it fits snugly inside the shell of the first. You need a fair amount of skill at metalworking to accomplish this, not to mention all of the proper tools, but the result is a clever deception that is hard to detect with the naked eye.