What kind of argument is this "only if they are in our own solar system"?
Even at the speed of Voyager 2, (15km/s), in a billion years it would cover about 4 * 10^17 km or about 40 thousand light years. I am pretty sure people who have been developing for hundreds of millions of years can do better than that, by orders of magnitude.
Also you put a totally strange assumption that all civilisations will only restrict themselves to visiting planets. If there is a lot of civilisation it is more likely they will have different motivations.