> It's hard to see how helping pigs stay healthy could have a negative impact on human health

I think that view underscores the differences in approach and beliefs in the US and Europe (not that both views aren't represented on both sides of the Atlantic, just distributed differently). The Europeans frequently have the view: Prove to us that this is not dangerous. Otherwise we prefer not taking the chance that you might be wrong. The US version in our eyes is frequently: "You can't prove it's not safe".

In this case you could risk introducing even worse diseases, who have previous been kept in check by the competition from the viruses you're now eliminating.