Why would you expect space to be any different?
So, assume only one of ten civilizations take the expanding choice early. That is still not enough to explain the Fermi paradox.
Unrelated rant/argument:
As a civilization we should publicise "anti heroes" as much as heroes. Those who e.g. destroy something beautiful for short sighted political votes.
Not just the politicians which destroyed our space future. Another example is the present political leaders in Iraq which seems to have caused a war just because they wanted to steal more without interruptions. Would they have done that if they knew their children and grand children would be in the news when their private jets land somewhere? ("Blood billionaires land in XXX, all better restaurants take a holiday. Sorry honest rich people".)
Edit: About the Fermi paradox -- the simplest answer ought to be that there are ET probes somewhere in the solar system and probably with lots of sensors floating around. The scary part is that they don't talk to us; that implies they are studying us and will clean the local infestation out before it spreads from the solar system.
Edit 2: The full argument (I didn't see it in the article?) is that there almost certainly will be lots of civilizations in the galaxy. We have no idea if we are among the first ten or among the second thousand. So statistics say we should probably be in the middle -- there are lots before we existed, we just can't detect them.
Maybe 10-90% of technological species do make themselves extinct by a nuclear war or an environmental catastrophe. It isn't enough. To explain the Fermi paradox needs a big killer, like an innocent looking physics experiment that sterilizes a solar system.
My point was that we could already be more than a one planet civilization. So all the eggs aren't in one basket.
To be clear: That we already could be an interplanetary culture implies that _if_ there is a big killer that explains the Fermi paradox, it is either big enough to take out a solar system -- or it is behind us.
The next stop for spreading to the galaxy would be to get outside the solar system. The good part is that the Oort cloud etc is a good training stop over. And it would also insulate humanity there from what happens closer to the sun.
(And directly a civilization is interstellar, then it really are multiple cultures (communication lag etc). Those will at least partly be "evolved"/selected for tendency to spread.)
Lots of other people since at least Fermi discussed time scales for spreading in a galaxy, it is an old discussion. If you really can't find good references comment and I'll check the usual suspects for references (centauri-dreams.org).
As I've mentioned elsewhere: Gamma Ray Bursts
I had missed the full argument. [Embarrassing :-)] The one I had seen was that closer to the galaxy centre there would be a higher frequency of supernovas per cubic light year, while too far out there would be too little of the heavier elements from supernovas.
The sad part is that we don't seem to have the interest either.