Well, the Food Chanel must be wrong, because they are completely different plants, with different botanical names. I grow fennel in my garden for my pigs.
Mine like lemon balm, but they like mint okay as well. Pigs that don't like mint might not like lemon balm. We planted a bunch of red clover out back and we put them out to graze when the weather permits. They grub on the clover. It costs maybe $1.50 for a big bag of seed.