The differential diagnosis for vomiting is huge...
Infection yes, but also headache, food poisoning ( as you mentioned) enteroviruses, motion sickness etc. Without waiting for the coroner’s report there is no way to know cause of death.
As a nurse who has given many vaccines the indication depends on whether the girl was febrile. Remember too that the general populations idea of what a fever is is different from the medical community. You are not febrile unless you have a fever of 100.1 or over.
Really? Then why do I feel so horrible when my temperature spikes up to 99? (It's normally in the 96-97 range.)