I wonder... does it *have* to trigger? Or can you choose not to have it do anything?

You mean if you don't care about the ring they picked or all the other rings have fate on them or something? I mean sure, it's a reaction you could just not activate the reaction.

The only forced trigger we have that I can think of Steadfast Samurai. Everything else is optional.

Well keywords must be forced triggers too otherwise the dishonor effect of Pride wouldn't make any sense. Or were you only considering actions?

In FFG-land, triggered abilities (starting with a bold designator such as Action or Reaction) are optional (unless the designator contains "Forced" or the rules say so - "When revealed" abilities are mandatory in AGoT, for instance). Constant abilities are mandatory. For keywords, the relevant factor is whether the rulebook definition contains "may": if it does, it's optional, if it doesn't, it's mandatory.