The answer is...it is a fact.
However, we need not imply that simply because dog dominance is a fact, dogs are constantly trying to "rule the roost," or that we need to eat first, go through doors first, never let our dogs sleep on the bed, etc. That would be circular reasoning.
Yes, dogs do form hierarchies. No, those hierarchies are not stable; they are contextual and change over time.
Dominance is a relative term, not absolute. Only very rare individuals are considered to be "dominant" all the time. Most dogs are not suited to being "alpha," and most of them realize it. When it comes to alpha, you either are or you aren't.
When it comes to individual behavior problems, leadership is absolutely essential. But what does that mean? Will a behavior problem simply disappear because you eat first, don't let your dog sleep on the bed, and always go through doorways first? Absolutely not!
It is important to set rules and boundaries. Good leaders do that, but these rules and boundaries should not be arbitrary. It makes no difference to a dog if you eat first or last. Service dogs are fed all day long in training and rarely have any behavior problems that could be attributed to "dominance." They often go through doors first, and I know of a good many highly trained service dogs that share their owner's bed—and even sleep on their laps in some cases. None of these dogs have "dominance" issues!
The shortest path to solving a behavior problem is to look at the behavior for what it is. What purpose does it serve? How is this problem behavior working for the dog? Are this dog's needs being met? What behavior would we like to see instead of the unwanted behavior?
Then we can set about making what works for the dog the same thing that works for us, like a good leader should.