Stop touching me!
They also say you cannot enter a rival's system unless you are at peace or have just won a space battle against ships in that system.
That's only if the system is occupied by enemy ships. You may freely enter a system where no other ships are present.
The info you presented is from the combat section of the rulebook. Go read the movement section of the rulebook. Specifically the section titled "Entering Rival Territory" on page 11. You'll see that the only restriction listed is when rival ships are present. If no rival ships are present, the restriction does not apply.