Are Mule Coins Possible Without The Help Of Mint Employees?

That is indeed impossible, because coins are always struck all-at-once, not one side at a time in a two-stage process.

A mule happens when "the wrong die" is inserted into the high-speed coin press that they use to make coins. Both dies (the "incorrect" one and the "correct" one for the other side) strike the blank at the same time, thus creating the mule coin. Human error is required for putting the wrong die in place, and as with many "human errors", it can be done either by genuine accident or deliberately. An accident is entirely possible, as the high-speed presses are designed to take any of the dies which the mint might use to make any of the coins requested of it; the same press might be making nickels today, and dimes tomorrow. Your typical "mule" is probably made when someone simply forgets to swap out one of the dies, when production on a press changes to a different coin.

How likely a mule-causing accident can happen depends in part on that specific mint facility's inner workings and processes - how dies for the different denominations and/or different countries are stored, catalogued and accessed, and how they're taken in and out of the presses. Is it just one guy who goes to the die cupboard and rummages around for the correct dies until he finds them, or are there multiple checks with multiple people making sure it's the right die before someone presses the "go" button? The more checks and balances there are, the less likely such errors can occur, and most modern mints have lots of checks and balances in place for this exact reason. But it should be note that "less likely" does not mean "impossible". Wait long enough, and pretty much anything physically possible will happen.

Double-obverse and double-reverse mules - coins that are either two-headed or two-tailed - are much harder to make by genuine accident, as the dies for obverses and reverses are physically different in size and shape - putting an obverse die into the reverse die position is literally like putting a square peg in a round hole. two-headed/tailed coins are almost always the result of someone deliberately fooling around with dies, in a coin press that isn't the usual high-speed production press but one which can be manually adjusted to take any old die in either obverse or reverse position.

The main problem with any "Error X must have been made by insiders at the mint to make money" conspiracy theory is twofold:
(a) how do they actually catch the "error" coins after they are made, when there's no human involvement or intervention in a modern high-speed coin press, and
(b) how do they smuggle the coins back out of the mint, when the mint has lots of security screening in place for mint workers which is specifically designed to stop those workers from smuggling coins out of the mint?

This is why I've always adhered to the idea that most mint errors (at least, in modern Western mints like the USA) are genuinely errors, that enter circulation through normal channels and are detected by regular people who happen to notice them in change. I'd find the idea that a mint error is a complete counterfeit, made outside of the official mint using fake dies, to be more probable than the "mint workers did it to make money" conspiracy.

Thanks @Sap - I tried to explain that, but cam up short on the words required to do that well.

Great explanation Sap. I always learn a lot from your insightful discussions.

to the CCF @ CKcollectibles2

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.