I emailed bitmex support and they said it is possible may have been accidentally triggered by them. However they did say they have no issue with the account and that "If you have any issues getting the account re-enabled and think we can assist further please let us know."
So Twitter may have shut down your account because Bitmex asked them to.
I don't really fault them because ultimately Twitter is the one at fault here, being the judge, jury and executioner.
Depending on what's actually happened it could be the case that Twitter are legally required to act. I don't think it's entirely fair to blame them until you know more about what's going on.