As there is no global government or other power, we can observe the relationships between people that have no common power and prove his assertion false.
For example, there is no one common power that controls all American and British people. Yet Americans and British people travel to each other's homes, have relationships with each other, trade with each other, and sometimes even move from one country to another. All of this is done peacefully, with no common power that controls both sides of the equation. Same thing with relationships between Swiss people and Japanese people, or Chinese people and Egyptians, or Brazilians and Indians, or anybody else that you choose.
If Hobbes' idea was true, wouldn't the relationship between two average people that have no common power be rather warlike rather than the mutually beneficially peaceful relationships that we see every day?