Basically, when you try to go online using the Switch, you need several things. I'm going to be summarizing everything from here but feel free to read it on your own time: https://www.reddit.com/r/SwitchHacks/comments/8rxg26/psa_strong_antipiracy_measures_implemented_by/
The first is a console that can go online. This one is easy and self-explanatory.
The second is your console's unique certificate. This step is to ensure banned consoles are not allowed online. This also lets them know who is going online.
The third one is a valid Nintendo Account. Account bans are rare and borderline legal since it contains your purchased titles, but it allows Nintendo an extra step of security when delivering bans while allowing people to retain their purchase history if their console gets banned.
The fourth step is unique to playing games online and requires a valid certificate/header but it does not pertain to your questions.
If you want to use eShop titles that you have legitimately bought on your banned console, you can use something like eXhop to download them since it downloads them from CDN, not the eShop. It turns out even if you're banned, anything downloaded with it will work as long as the console can verify that you purchased/downloaded it which you can do by accessing their website if you are console banned. Its their way of allowing you to retain all your purchases but prevents you from using hacks online (without buying a second console).
As for proof, whatever you suggested is actually more than what most people provide (which I'm saying is a good thing) so please do so. Maybe add in something into the video so we know its you like a piece of paper with your username or something. Be creative and surprise me
