Josephine had personal experience (as a vet tech) with serious problems concerning pyrethrin use. She's posted about some of the products that have killed cats and other animals.
You don't have to dilute the Advantage. Measuring like Mum suggests should work well to apportion it among your pigs.
The vet had obviously never read that page here- I think she's scanned the site before but nothing in depth. She's very interested now to see the collected experience!
To be honest, I'm like the vet. I trust the scientific method to sort things out when it comes to this sort of thing. She learned in school that this was safe, it's been safe so far in her practice and now she'd like some science backing up her decision to change. I bet she'll find Josephine's postings. I found them!