Sara;

I must agree with your inspector. All laboratory personnel work with hazardous materials be they biological or chemical. It is simply negligent for lab management not to enforce the wearing of lab coats and other protective clothing and equipment to protect the staff from accidents that will occur.

I must also agree in the matter of jeans and other too casual clothing. Patients and visitors have a reasonable expectation that they or their family and friends will receive professional, competent and compassionate care. This expectation is violated when hospital staff dress like manual laborers. 

It is never a mistake to have high standards for the lab staff be it in dress or in any other matter. 

"Treat a man as he is and he will remain as he is. Treat him as the man he could be and he will become that man."

Respectfully;
Donald Andersen