If part of your "competitive banter" involves calling someone an "idiot", then you're doing banter wrong. If you want to have your chat logs peer reviewed and have your punishment properly explained, you'll have to submit the chat logs associated with your punishment.
That said, in my experience, a lot (and I do mean a disconcertingly large number) of people don't actually know what banter is, and assume it means insulting and harassing whoever you're "bantering" with. That may be the case with exceptionally close friendgroups/siblings, but in the context of dealing with random people in a game like League, that doesn't fly.
Here's the definition of "banter", as pulled from Google.
Banter
noun
- the playful and friendly exchange of teasing remarks.
verb
- talk or exchange remarks in a good-humored teasing way.
"Good-humored", "playful", "friendly", "teasing". Those are the operative words, and if your chat falls short of those descriptors, then it's not banter.