Imagine sending your child to school and thinking that he or she will have a good day; you expect it to be safe and for everything to go well. Then, you get a phone call that your child has come down with an illness, so his or her blood was taken and sent to the lab for diagnosis. Once the diagnosis comes back, it's a shocking report of an illness there's no way your child could have. Now you have to face the stigma that comes with it.
After you take your child to his or her private physician, you find that the test results were wrong. Not only that, but your child had tests performed on him or her without your approval as his or her parent. Shouldn't you have been informed before blood was drawn, since it's an invasive procedure?
A case like this took place in California, and while there are some varying laws in California versus Florida, unless you've signed a waiver allowing the school to treat your child with medical procedures without telling you first, it's likely that it was against the law for the school to take your child's blood.
As a parent, you're entitled to make decisions about your child's health. A simple fever doesn't mean much except that your child may have had a cold or flu, so taking blood is an unusual step. Similar to this would be giving your child an inoculation without your approval; that in itself takes away your right to decide if you want your child to receive vaccines or not. If you didn't give consent to the school to treat your child, then the school could face charges of battery or be accused of medical malpractice.
Source: SF Examiner, "School must contact parents when performing certain medical procedures" Christopher B. Dolan, accessed Feb. 12, 2015