seems like youre the one holding a grudge here. i havent seen the info on why you were banned but i can tell you that no one is going to give you a reason for punishment for another player. and yes you could mind your own business if slacker jailed or banned anyone he had good reason. Its not like he goes looking for people to ban. If you have bedrock because of an afk machine then you can live with it. thats what you get for having an afk pool it happens to everyone who does it not just you.
As for your screenshots they dont show much except that you didnt want to drop it, and that you got mad an admin was in your base(which they have every right to do). Admins deal with people everyday that are angry that their friend or their other account got banned, so when you sit there and pester someone simply because you didnt agree with them they will ban you as well.
If you truly didnt agree with the decision then in chat was not the place to handle it, here is. So maybe next time drop it ingame since its not going to help anyways and have the person who was banned appeal it. Not sit there and throw a fit ingame untill you get banned as well. Its not up to you to investigate the ban and decide if it was justified or not. And no admin is going to entertain those kind of actions ingame.
If someone really got banned for no reason then they can appeal it on here, not have their buddy try and be their lawyer