I don't know that I would say that it is "more than likely" a hatchery fish, just because you can't tell. It's that attitude of always putting the burden of proof on the wild resource that has led us to where we are. And a spot on the ESA list is not the only index of whether a population is in trouble, its just the index of last resort, right before extinction. We should try worrying about our fish BEFORE they make the list.
While there's been too little work on it with steelhead, there's plenty of reason to believe that these very big fish, as rare as they may be, contribute to the productivity of a population at a rate disproportionate to their numbers, particularly during times of low abundance. If they are part of the population, especially if they're rare, it's for a reason, and it's likely not to wind up on someone's wall or in their smoker.
That said, I don't actually know what the status of Quinault steelhead is, and it certainly is true that the Quinaults have rights to net the river. And it is a beauty.