This US site suggests that daisies can be toxic to dogs but that they're not in the 'drop down dead' category:
https://www.1stinflowers.com/articles/poisonous-plants-for-dogs.html
I suggest your friend should keep an eye on Fido and contact a vet if he seems unwell. However, given the rubbish that most dogs eat without coming to any harm, I suspect that he'll be fine anyway.
(Incidentally, an old name for the ox-eye daisy is 'dog daisy'. I wonder if that's because they were known to be attractive to dogs?)