To be honest, perhaps I'm underestimating people's intelligence, but it is my suspicion that not too many people associate "swine" with "pigs".
It's not a common word for pigs. It's archaic.
I'll bet there's a fair number of people who hear "swine flu" and never even realize that the word "swine" means "pig".
And I'll bet there's an even greater number who hear "swine flu", do realize- vaguely- that "swine" is an old-fashioned word for "pig", and then promptly forget that fact and never make the association again.

I understand why the pork industry is so desperate to have this stigma removed from their product, but frankly I think they're worried about nothing.
If it were called "pig flu" or "pork flu", there might be a problem, but as it is, I doubt there is one.