Fascinating discussion here! But it may have had participants worn thin by slipage across epistemic boundaries. Each of several epistemologies might have been useful to assess the situation, but frustration might have crept in because we didn't agree to one. The operating paradigm, or frame of reference for solving the problem, was a bit fluid. In this conversation, I can think of 4 distinct epistemic frames that could have helped:
Scientific Causality. No one picked up the empirical torch, and perhaps rightly so, because trying to reproduce numerous scenarios of low-level players and foul language and repeat suspensions would be tedious and unproductive. But causation appears in the question header. Could we produce a trend empirically? Perhaps. But could we prove cause and effect in this manner? Doubtful. As is the case in most soft sciences like psychology, there are too many variables at work (as mentioned, impact of repeat offenses, opinions and stress levels of game admins, behavioral quirks) to prove a result. More on behavior below.
Philosophic Logic. Lukas weighed in heavy on this front, and while I am not a student of logic, it seems the conclusion or C1 of suspension could be caused by P1+P2+P3 or by P3 alone. P1 and P3 are observable. P2 is an unsupported opinion. While it is possible that P1+P2+P3 caused C1, P3 operating independently at any time could also cause C1. Would "probable cause" in a court of law say Coltonoscopy was guilty? Only if prosecutors could prove P2, and disprove the possibility of P3 in isolation. The defense rests. On an interesting side note, when Labreuer raised the stakes via the DUI parallel, the analogy of an errant accomplice might hold up: that is, a well-meaning friend who bought the suspect one too many drinks. Would an ensuing DUI be his fault? Again, the drink may have increased the likelihood (and in the eyes of our society introduced some ethical culpability) but it would be difficult to prove cause or assign full blame. As framed in the original question, such factors are circumstantial, not causal.
Philosophic Ethics. Coltonoscopy, you were laser focused on the ethical question of whether the bad-mouthed friend had a right to blame you for actions that he himself had taken. This is an accountability question, which is difficult to counter. I for one would agree, the bad-mouthed friend was behaving inappropriately to both the gamers (foul language) and to you (projecting blame for his own actions). Perhaps time for a new friend? Your frustration, I think, may have been because you intuitively (and perhaps deeply) sensed that the blame wasn't fair. Wouldn't that be like Descartes, using rational thinking to get to the answer that seemed right to him, given the situation?
Complexity. Another applicable frame (my favorite) was also not invoked, but its one that matters greatly in soft sciences (like psychology and sociology) and it applies here for the very reason called out by Mike early on: "dealing with an ego." In this case, we are dealing with complex behaviors that are not governed by strict linear causality. Humans typically adapt their behavior in social settings to get what they want. If we grant Lukas the veracity of P2 (not that I have, mind you!), we would say that Coltonoscopy may have created an initial condition that could potentially increase the chances of C1 (suspension), but in no way could we say that he caused it. A complexity frame would never assign such an outcome a cause, owing to the emergent and adaptive behaviors of the many interdependent agents in such systems. People are unpredictable. Especially dysfunctional ones, who blame their friends for their own misgivings.
My understanding of causality follows a thread from Bacon/Newton to Hume to Kant and I can't say I have it completely figured out. Complexity perhaps could get us to an answer the fastest. But I think choosing any of the frames above would eventually release Coltonoscopy from blame.
The takeaway? For me, it's that we can reduce churn in our critical thinking (arguments, discussions, philosophical debates) when we put thought to which epistemology best fits the situation at hand. We're effectively deciding which rule set is most likely to get us to a useful answer for that problem domain .. quickly. Perhaps most of all, we need to pick one, declare it, and stay with it.
Is any one method right or wrong? That sounds like another metaphysical question .. for another day.