Not a lawyer but I'm suspicious about that: first of all, I don't think downloading is actually illegal, it's either sharing stuff without license or keeping stuff without license that are generally illegal (which is why viewing movies from an illegal streaming website is legal in most places even though the website owner is clearly doing illegal stuff).
Then, if you have a license and the law in your jurisdiction allows personal backup, I think you'd have the right to actually store the thing, so I don't think you'd be breaking the law here.
People also say “No copyright infringement intended” while uploading full movies to YouTube. People, especially when it comes to matters of copyright, typically have very poor understandings of law...
Moon Channel (an actual lawyer) has a fairly clear and concise summary with particular relation to the Dolphin emulator’s attempt to get itself on Steam: https://www.youtube.com/watch?v=wROQUZDCIMI
You are in the clear if you download it from a ROM site (and own the corresponding cartridge). You are not in the clear if you use filesharing, unless you freeload.
Edit: you edited your answer after I replied, so I'll edit mine too, it shouldn't be illegal to download the ROM if you physically own a copy. If you want to do it the hard way, buy a GB dumper.