Fire service is definitely excludible (not on the subscriber's list -> we're not putting your house fire out) and arguably rivalrous (a team of firefighters cannot be in two places at once).
In most areas, fire spreads uncontrollably. Even if I don't buy firefighting services, I benefit when firefighters put out your house fire and prevent it from burning my house down. That's the non-rivalrous and non-excludible element.
But you are absolutely right under some circumstances - in a sparsely populated desert, firefighting would be a private good.
