Are Mule Coins Possible Without The Help Of Mint Employees?

I would suppose that the mint operators would place the incorrect die in place then just "test" run a few planchets, before properly setting up the machine. (but that would just be a guess on my part)

Indeed, if a "mule" setup was indeed placed into a normal production high-speed press, then thousands or tens of thousands of mule coins are likely to be made before the error is noticed and rectified - or indeed, the situation might remain in place until one of the dies breaks and needs to be replaced.

Many of the more famous "mules", such as the Australian 10 cent / 1 dollar mule mentioned earlier in this thread and the New Zealand 2 cent / Bahamas 5 cents mule from 1967, do indeed occur in the tens of thousands (though precise mintages are usually unknowable). A mule that is only known from a dozen examples or fewer, despite broad publicity about the mule's existence and every roll hunter out there actively looking for them, should indeed garner suspicion as to why there aren't more of them.

Proof mules are a completely different thing, since proof production is a lot slower and more hands-on, and tiny numbers are to be expected in such cases. Again, to use an Australian example, some 2006 proof sets have a 1 dollar coin struck using the old 2005-dated obverse die, thus creating a mule (since the 2005 and 2006 proof dollar coins have different reverses, the 2005 mule is obvious even if removed from the set). An easy mistake to make, given that 2006-dated proof sets would have actually been produced in mid-2005. I believe only five or six mule coins were produced before the error was noticed and corrected, yet the mules still escaped and were sold as regular proof sets. Example on eBay.

I suspect it would also depend on the dies in question; if the incorrect die were significantly the "wrong size", larger or smaller than the coin being struck, then I suspect this could place extra strain on the machinery and might cause one of the dies to jam, break or otherwise obviously malfunction in such a way that the process stops after striking just a few coins. This isn't always going to happen (the Australian 10 cent / dollar mule an obvious example of a "wrong size" mule) but it might help explain things for certain mules.

The other warning flag would be provenance. "True error" mules should essentially be shipped out with the rest of the freshly minted coins, and thus distributed randomly across the country, or at least across a specific city or region where that batch of coins containing the mules was shipped to. Once someone finds one and it hits the numismatic news, they should start popping up everywhere, at random. But if one single source seems to have acquired all of the mules of a certain type, or they all ultimately can be tracked back to one person or a small cabal of associates, then we likely have a case of either mint shenanigans or counterfeiting.

It's been 66 years and still only one known example of that mule has surfaced, so I'd assume it was a counterfeit. Which does seem to be the consensus, despite an official government pronouncement it was genuine.