This is what happens when I make other people's arguments: I tend to screw them up.How could it be technically impossible when it happens naturally? Over the time frames involved the natural velocities of comets and the stars themselves are sufficient for a lot of migration.
Personally, I think that interstellar travel is quite possible and something that we are likely to partake in at some point in the future.
I guess what I'm suggesting though is that it may be impossible for intelligent lifeforms to send themselves to other stars. But to be honest, when you put it like that I can't really agree with that. So, I will modify my statement:
Interstellar travel may be so difficult to engage in that no technological civilization has engaged in it, regardless of how many there have been to this point in the history of the galaxy.
It may be so difficult that while some civilizations do engage in it, they don't get very far: they travel to one or two other nearby stars, perhaps, and don't go further because they find the rewards aren't worth the effort.
Or it may be that civilizations, once they reach the stage that interstellar travel is possible, simply tend not to be interested in interstellar travel.
Personally the Fermi Paradox does modify my guess as to the probability of ETIs in our galaxy, in such a way that I think it's less likely than I did before I'd heard of the Fermi Paradox. But it certainly doesn't modify it all that much, because there are so many possibilities other than "life is rare" that explain it.