Can an EEA Family Permit for UK Be Refused if the Person Has a Costly Disease (Such as Cystic Fibrosis)? ?

My wife has cystic fibrosis and we are applying for an EEA Family permit (I’m Italian), so that she can join me while I do my PhD. We are entitled to NHS treatment as I’m a full time student and we also have a private insurance from the institution where I’ll be doing my PhD. The private insurance will cover her CF. Can they deny her the family permit on the grounds that her sickness is expensive to support (though under NHS treatment + private insurance, most of it would be financed). We have 1500 pounds monthly for our living expenses.