I haven't rented to someone with a service animal, but I have looked into the laws before when I was thinking about renting. What she seems to be referring to is more along the lines of an "emotional support animal" than a "service animal". An emotional support animal is provides emotional support but is not trained to perform specific tasks to assist the person - the animals mere presence provides emotional support - whereas a service animal is trained to perform specific tasks (like a seeing eye dog, medical alert dog, etc.). As far as I know, cats can't be service animals but can be emotional support animals. For an emotional support animal you have to have a letter from a mental health professional stating that you have a disability/ disabling condition (so I think her anxiety would have to be relatively severe to be eligible) and that the emotional support animal provides therapeutic benefit. And if she wanted two or all of her animals to be considered emotional support animals, she would need separate letters for each one essentially stating they are all necessary.
A long explanation, but basically it is relevant to the rental situation because emotional support animals are allowed in "no pets" rentals, and landlords can't charge extra rent or require an additional damage deposit on them - they are seen an an accommodation for a disability, not a pet.
Honestly, this seems like an odd situation - why would she want only two certified? Because the landlord has a two pet policy and she wants the other two to not "count" as pets? This is probably a legal grey area and the landlord will probably allow it to avoid a lawsuit.