So, without seeing your chat logs, I can only speak generally, but here's the biggest misconception in your post:
It does not matter what the "context" is - it does not matter what anyone else says, or does - you are expected to remain non-toxic and not flame, harass, belittle, or be abusive towards others. Ever.
Many people think that it matters if someone is inting, or if it's "joking", or if it's only directed at one or two people - it doesn't. The thing is, you may have been joking with a few others - but there are 10 people in the game, and if not all 10 are okay with it, you are not allowed to do it. Even if all 5 enemies are okay with it, your teammates may not have appreciated your "joke" flaming - and thus you were validly reported. If something is toxic, it remains toxic even if others are doing it.
The only time it is acceptable to do something that is otherwise against the rules is if all involved (i.e. 4 teammates if in team chat, or 9 others if in all chat) are okay with it and do not report. The second someone is not okay with it, they are certainly allowed to report and you will be found at fault - as it's against the rules.
One analogy is this: If the speed limit on a road is 60 mph, but everyone consistently goes 70 mph, it's not likely that anyone gets pulled over. But the second there is a police officer involved (i.e. the second someone reports), you're going to be pulled over and likely ticketed. It was never okay in the first place - but if everyone was doing it (or okay with it at least), it flies under the radar. Once someone complains "these people are speeding on this highway" and the police get involved, it's no longer okay.
edit not sure if you'll see this because it's an edit, but here's this as well:
You are certainly able to write in to Riot Support and ask them to review the suspension, at which time a real human will review your logs, your history, and the entire game. Note, however, that if you did flame, and if someone reported you, they will not go to great lengths to ask the player "did you really mean to report DarkBalls?" If you wish to argue that everyone in the game was okay with it, the onus is on you to have every single person who was in the game write into Riot Support and rescind their report (if they reported) or confirm that they would not have reported you for the action. Even then, considering there was originally a valid report, it is up to the determination of the Support agent to decide to either uphold or rescind the ban - they will base this on the circumstances.
The bottom line will be that you did something against the rules, and at least one player reported you for it - thus even if that player now regrets reporting you, they were affected by it enough at the time to decide to report you. But there have been an extremely rare case or two where a player gets all others in the game to confirm they would not have reported and/or rescind their reports and Riot decides to remove the ban.
