There are some animals in the west that will kill your dog if given a chance. Coyotes will lure a dog out and the pack attacks it once it is away from its humans.
Rattlesnakes very from problematic (diamondbacks) to quite deadly (mojave green), depending on where you're talking about, and will lurk in shady places or lay in the sun, depending on the weather.
In some areas in the west, javelinas roam and are quite capable of attacking and killing a dog.
Mountain lions and bobcats will attack dogs as well.
Bears can be a problem and dogs end up dead because they rush forward to confront the bear and protect the human. In most cases bears don't attack humans, unless you go to grizzly country.
You need to know what the local conditions are where you are going as "the west" is a huge area and some threats are greater in some places and less in others.
The terrain also plays a part as far as visibility and knowing what is or is not around.
Weather conditions not just in the immediate sense, but as far as good years/bad years for game (CA is in a huge drought, for example) can make wild predators hungrier and much more aggressive.
Finally, if you cannot absolutely recall your dog off of ANYTHING in an instant... then you're just begging for trouble. Squirrels and rabbits will abound in wilderness areas, and there's the coyote issue as well. Even a well-trained dog that has not been proofed on such temptations is very much at risk when first encountering them off-lead. Boondocking isn't the time I'd choose to start those lessons.
So... pretty clearly, the safer bet is to keep your buddy safely tethered to you in wilderness areas. You will have the final decision, of course. Personally I've had dogs off-lead in shall we say "wilderness interface areas" but those were under conditions that I knew and understood from living in the area. In a strange area where I don't know the risks on the ground I would be much less likely to do so.