Evidences of banned accounts on Steam (you can check the users profiles, not just the messages, apparently you can't even click with your mouse), but you call it fake... at the same time you pretend that people will believe your words... oh lord!
Now you admit that you have been banned one time with a detected cheat, but then you have used it again to be banned a second time.. and all of this on a "family shared account"... seems perfectly legit.
Someone with multiple bans in this game, trying to teach others what's safe... the irony. Are you sure you want to help the community? To me it looks like you're trying to make them all banned, because what you're posting is false or completely wrong at the best, and I have already said to you why.
To anyone else: don't listen this guy, if you're BE banned with a "shared account" linked to your main account, you will not be able to access to that game, neither with your main account. And this is a fact not a guessing: don't trust any random user on internet (including me) just use Google and type: "steam ban family sharing" and educate yourself.