AFAIK it can be done anonymously, for a tiny price and a bit bigger bounty (if found). Since the state of the channel is private, watcher has no information about anything anyway. On top of it - it's only a secondary defense. Your wallet still can do the monitoring by themselves and other party can't know that you dissapeared from the internet and won't appear in next 24 hours in advance. Other party risks reputation and their own funds if they get caught by you or your watcher(s). Because of that attacks like that are very infeasible.
