Josh did do something wrong. He failed to perform due diligence and failed to keep proper records of vehicles in his possession. He's lucky the police aren't going to press charges, he isn't vindicated. Yes, he wasn't deliberately laundering stolen goods but he was actually, through negligence, laundering stolen goods.
Ed, like Josh, was tricked into complicity in selling illegal goods. Like Josh he failed to perform due diligence. Unlike Josh, he recognised the problem and stopped, by himself. He wasn't investigated by the police and there was no publicity.
Whereas Ed was motivated by financial desperation, Josh was motivated by laziness. (You could argue greed in both cases). But Josh had the opportunity to do his paperwork properly, entirely at his leisure, whereas Ed did not have it within his power to discover and rectify the problem with the operation he'd become involved with. His only option was to leave - and that came with penalties - but he braved it and did the right thing. Josh on the other hand buggered off to Thailand and left his mess for Rex to clean up.
So yes, Ed's illegal activity happened to be more directly incompatible with Home Farm but that's chance really.
The nepotism test is to consider what would happen if a Grundy boy had done what Josh did. I don't think he'd be welcomed back onto Home Farm, or anywhere, so fast - because rather than 'one mistake, he's a good lad really and we need his skills', there would be a sense of 'reverting to type, can we really believe he won't do it again, or bring unsvaoury people onto the farm'.