What's wrong with that phrase?
The whole point to veganism is to avoid eating animals or anything made by or from animals.
Probiotic foods are made of animals. A live culture of teeming, tiny animals feed on the raw food and partially digest it, making it more nutritious for humans. These little critters include symbiotes beneficial to a healthy microbiome. (The human body is not actually a single organism, but rather a communal body more like a walking ecosystem. Try not to be a vengeful god to your symbiotes.) So probiotic foods are live foods. They're good for you. But because they are full of happy little animals, I would never call them VEGAN.
This is likely another example of humanocentrism, which is why a lot of people will eat fish or even chicken but not mammal flesh. Yet vegans often get all high and mighty about how they don't eat animals. Folks, if you're eating probiotics, you're eating swarms of animals -- they're just too small to see easily. If the idea of eating animals is gross or sad to you, skip the probiotics.
Me, I love the stuff because it is live food. I have further discovered that the more different cultures, the better. Brown Cow yogurt, which has 5 cultures, does a much better job than most brands which only have 1-2.