Your statement is wrong.
I'm not making a statement, merely asking the question.
There is such a thing as the presumption of innocence. In order for Charlie to accuse of complicity need to have evidence that he was unaware of the illegality of the transaction.
People often conflate those two things. The presumption of innocence simply means you are innocent until you are proven guilty. However, in the eyes of the law, being guilty generally doesn't depend on whether or not you knew you broke the law.
Ignorantia juris non excusat. In the scenario I've posed, I stated that Charlie may not know what was being purchased. That part was central to the premise.
The seller of weapons in the store is not complicit in the murder if he legally sold the weapons to future murderer.
If the weapon was purchased legally, then that's not a relevant example. In this example, if someone wanted to buy a gun
illegally and it could be proven by law enforcement agencies that they used your money to obtain it, what are the legal implications of that? Could you be arrested? Charged? Could there be a lengthy investigation that essentially puts your life on hold until it's resolved? You don't even have to be found guilty for it to potentially have a negative impact on you. I just want to understand, legally speaking, what the potential complexities are.
I don't think so. It's basically similar to you having a full node that is the first node to push a certain transaction (not one of yourself obviously) to the network, where that transaction may have been initiated by someone buying a huge load of drugs, or whatever other horrible acts of crime. If Charlie is legally complicit in the crime, then your full node pushing that drug or whatever transaction to the network too. If I wire money to you to finance whatever illegal activities, is the bank then complicit in the crime as well? No.
The functions of a full node are largely automated and you don't have any financial interest in the offending transaction, so that's still not quite the same thing. With Lightning, the funds on your channel belong to you and you have to sign the transaction to permit the payment to go through. However, I think you salvaged it with your second example of wiring money and the bank not being complicit in the crime. That sounds like a much better answer and far more closely analogous to the scenario posed.