My son went to the school nurse last week because his throat hurt. I picked him up, took him home, checked his throat, gave him some meds & waited. By that evening he was fine, but about two days later came down with a cold.
Today he went to the nurse to see about getting some cough drops (he has a cold, one that all three kids have had this week) & the nurse proceeded to check his throat & declared he had strep. Even though his throat doesn't hurt. She called me & said I have to pick him up, take him to the Dr & he can't return to school without a note from the Dr. She said he had white spots in his throat. She would not even let him go get his things from class.
I had his sister (thank God she was home today) take him to the Dr & the strep test is negative, just as I knew. There was also no sign of white spots. Even the Dr thought this was very extreme for the nurse to do. Needless to say after the time, money & him missing class over this I am a bit ticked off. I could understand if he had a fever, or was even complaining about his throat, but neither was the case. So yes I called her & let her know that he does not have strep & until she obtains an MD after her name she should not diagnose people.
At the beginning of the year my DD went to the nurse because her ear hurt. The nurse said she had severe ear wax & I needed to flush her ears out. I knew something was wrong since she never complains of her ears. Went to the Dr & sure enough she had an ear infection. The Dr said it was good that I did not flush her ears, it would have been extremely painful.
Congratulations on being "that parent".

The nurse is there to help your child, and also to protect the other children from catching what your child may or may not have. Did she TELL you your child had strep throat? Who did she "declare" it to? Is it possible she suggested it could be strep throat and your child gave that to you third hand and maybe phrased it differently? Big difference there, wouldn't you say?
And it sounds like your kid goes to the nurse a lot. If he had been sick over a week, like you mentioned, he saw her last week with a sore throat and then went again this week, I think it was reasonable for her to think he needed to see the Doctor.
As far as your comment, you owe her an apology. Perhaps you should have your kid call you when he needs cough drops.