You don't have to prove that that money is obtained legally. You do have to refrain from knowingly transacting with illegally obtained money. If a reasonable person would be aware that the money you are handling is not acquired legally, you can be found culpable.

You can say it's "not your job" all you like--if you are operating in the United States, you are not correct and it would go very poorly for you to try.

Yeah but in order to do that they need a warrant. If you're moving around money like that, it's very likely you got that money illegally. I'm no fan of the police, but sometimes following the paper trail is the only place to start an investigation. I'd rather the police be able to get a legitimate warrant to investigate something than have them operate in lesd than legal ways.