EXACTLY! I say: "I am here with so-and-so, who is not feeling well. They said they talked with you about it this morning and you said you could pick them up if they could not make it. Well, they are here now saying they 'cannot make it,' and are unable to tolerate *sitting in class."
*When a kid has no measurable clinical signs of illness (no fever, no vomiting, looks "fine," etc), I use this statement as a barometer. Can you tolerate sitting in class? If yes, then go sit in class. If no, then I will call home.