I understand your position. But (there's always a "but") I have a friend whose kid is severely allergic, their daycare didn't take it particularly seriously(!), for reasons similar to yours. So of course one day there is a PBJ near the kid, he has a crazy reaction, the staff call the parents "we're afraid to use the epipen" at which point the mom hangs up and calls 911 herself, invoke FMLA and has to hightail to the ER
"The Family and Medical Leave Act of 1993 (FMLA) is a United States federal law requiring covered employers to provide employees with job-protected and unpaid leave for qualified medical and family reasons." (Wikipedia via Google)