That's one way to see things. But when I think about a civilization with enough technology for interstellar travel, and considering how far we are from this, I realize that Hawking ignores many aspects.
The entire idea of one civilization conquering other's territory is based on assumption that outside explorers are interested on certain resources like precious metals, minerals, specialty products such as plants and herbs, cheap (slave) workforce, and ultimately land to setup bases or use as alternate home. But for the benefits to be greater than losses, traveling must be cheaper and less risky than doing whatever other thing that could produce the same results.
Now that we are aware of this economic aspect, let's ask ourselves: How difficult is interstellar travel?
Let's start with the basic fact that we don't know how to make interstellar travel. We went once to the Moon, then we gave up for many decades, probably because it was not so useful. Recently we went to Mars, but not ourselves - we sent robots there. Of course they are advanced technology, but still quite far from what's required for large scale colonization.
If you are physics enthusiast, you probably know about huge problems of interstellar travel. The greatest issue is by far the distance. The Voyager 1 probe left Earth 36 years ago and have reached about 130 AUs (Astronomical Unit) from us. The closest star, in comparison, is about 270,000 AUs away. In the current speed, Voyager 1 would take more than two thousand years to reach that star, assuming it won't fail for radiation or another glitch. Even if we could go 10 times as fast, it would still take 200 years. No human being is known to live nearly as long.
Even if we develop some hibernation technology, the most we could do with current advances is send a small team of scientists. What could they do when they reach another planet? If we find a race as advanced as humans (with a pretty active weapons industry), then trying to conquer would not be reasonable.
Now let's consider what could be easier to achieve than interstellar travel. We have a quite automated manufacturing processes, we are developing 3D printers, we have a rover on Mars that can understand high level commands, and soon we'll have commercially available self-driving cars. The conclusion is that we might have robots that replace humans in almost any task. This precludes the desire to find a race useful for slavering purposes.
Automation and AI is also the key to solve resource problems. For instance, if we want gold, silver or other precious stones, we can just send robots to an asteroid or one of Jupiter's moon, and setup an automated mining facility there. Or we can go further and build a fusion/fission reactor that is capable of synthesizing any element we want. Remember that a lifeless moon or asteroid millions of miles away from Earth has very relaxed environmental issues.
The same automation can be used to build a base on a inhospitable planet, full with greenhouse crops and carbon removers, or even to change a planet's atmosphere by installing huge high-performance filters. This means that an advanced alien race probably won't need Earth to live. They could simply grab a nearby inhabitable planet and artificially fix its climate towards their needs.
Now let's talk about Earth's unique features: our biological matter such as plants, herbs or maybe exotic pets for a galactic zoo! They are unique because in other planets, life will probably evolve to different forms. Here at Earth, we have reached a level of genetic manipulation that easily allows us to engineer new species. We are even entering a stage where we can change DNA of adult people. This means that if an alien wants a sort of biological stuff from us, there is no need to extirpate entire populations - they only need to grab some samples of whatever is close to what they want, go away and adapt. If you are worried about being hijacked by aliens, don't - chances of being hit by lighting are far greater. And if you get hijacked by aliens, remember the unique opportunity you'll have: it's better than becoming an astronaut!
Even if aliens take Earth as a sort of galactic tourist destination, they won't vandalize our planet the same way we avoid destroying natural reserves. But most likely, with advances in device-human integration and brain understanding, a better option for advanced aliens can be creating a kind of matrix computer and simulate the entire Earth there - no need for distant travels in economic class, with small space for legs and terrible food! Again, there is no need for they come around and take over our planet.
I'm agnostic. I'm not sure if there is a God or not. But it's clear that current stage of human civilization could not overcome the urge for engaging into wars from times to times. Maybe interstellar travel is somehow "designed" to be as hard as possible, so that only after a race overcome the futile fight for resources (which is the main cause of wars), it can reach technology necessary for visiting other habited worlds. This way advanced civilizations become naturally unwilling to destroy each other.