If local staff don't bring it up, then maybe a Supervisor who is part of the particular ARTCC/ATO/whatever will, if they witnessed it. Or maybe one of the individuals involved in the incident wishes to request a post-factum investigation (or a witness reports it, etc. There was a reason I said "I.e." because there are plenty of examples). If we want to stick with the ARTCC example (assuming that's what you're most interested in considering you're representing yourself as a member of the Houston ARTCC on this forum), if someone says something distributing, infringing, obscene, vulgar, profane, or unlawful (use your imagination here, you wouldn't believe what some people will say to each other), but they are on an VATSIM ARTCC TeamSpeak server, are you saying that the VATSIM Code of Conduct shouldn't apply? They are VATSIM subsets and, therefore, fall under the CoC and all other policy/regulation.
And, no, CoR 6.01(b)(9) does not end in "blah blah." I'm not going to cite the full text here because it's readily available, however, the focus isn't on your computer, it's on you (the member). Hence, "which are utilized in any way by VATSIM.net members for communicating . . ." So, if you're in an officially recognized VATSIM organizations TeamSpeak engaging in public discussion, yes, you fall under the CoC and all other policy/regulation.
As for the exact wording? I don't write the rules. I'm simply explaining to you why they apply in these situations. If you're looking for a debate on wording, you're on the wrong forum, as no one hear can change that (not that it should be changed in the first place).