The buyer claims that the product is counterfeit after receiving the product and asks for a refund

I have been mulling over this one all afternoon. 

Just going by your description around the circumstances of how they were first purchased, it sounds like they could be counterfeit, I don’t know these products myself, but if we were talking about a designer bag in this situation I would say 100% counterfeit. 

If he has sent a dispute report before emailing you, then that is a bit aggressive, but that’s out of your control, and they are allowed to do that, although I would argue that is not the correct etiquette. 

So to your questions -
Yes buyers can rely on their own experience, for all you know, your buyer (or any other buyer) can be a hard core collector, that can spot the fakes from a mile away ( For example for me, I would not need to take a WWI German Iron Cross to antique dealer for verification, I can spot the fakes, and prove they are fakes quite easily.)  

"How does the seller need to prove that the handle is genuine? Can an unopened picture of the package and original proof of purchase be used as proof?"- So with my own experience I had a similar situation with a Michael Kors bag, so I just reached out to Michael Kors, and they helped me. Perhaps Nintendo would be gracious enough to help you. 

Honestly I would be refunding him, you would also be paying for return shipping, as well as his initial shipping costs (Or you refund him shipping and purchase price, and then tell him to keep it so you don’t lose out paying for return shipping). 

So I understand that this is probably not the kind of stuff you were wanting to hear when you posted your question, just remember I am trying to help, but I do suspect that these are not genuine. 

For your questions.

1. Yes, if a buyer suspects an item is counterfeit they can query that. That is their right to do so. But they should at least do some basic research first themselves to solidify their suspicions.

2. Yes, a receipt from a reputable store is what TM will ask for, and will suffice as proof that the item is genuine. The problem in your case is going to be if Trade Me will accept a foreign receipt in a different language. You would probably need to provide supporting evidence as well. Highly unlikely they will want to mess around doing translations etc.

General. It is worth noting that the Monster Hunter special edition controllers are available from Chinese websites, and are clearly counterfeit, going by price alone. So your seller would have to be very very certain they are genuine. Can't find anything about spraydon 3 so that's a typo no doubt? It might be worth them posting in some gaming forums with photos of the ones they haven't sold yet to get an opinion from people who really know about these things. Could even be worth asking Nintendo themselves. 

Hi there Frank! Thank you so much for posting. Buyers can totally rely on their own experience. When it comes to sorting out disputes, we just need some concrete proof to back up what the buyer and seller are saying. That could mean showing us the original receipt or any official documents - even if they aren't in English, but make sure they are accompanied by an original document with an English translation to confirm that the item is genuine.

As a buyer who was recently sold an obvious counterfeit laptop charger, it was extremely frustrating to have the seller repeatedly deny it and then ghost me over it. I sent photos of the item and an explanation of how it differed from a genuine product (fonts, etc of writing on the side of it were wrong...). They refused to give an explanation for the differences, instead only repeating that it was genuine.

If i were you, i would advise those people to pay attention to what the buyer is saying. Ask the  buyer how they know it is counterfeit