Pharmacy insurance policies offer cover for employer's liability. e.g. if an employee has an accident at work, say falls over, gets a needle prick injury or gets cut by glass or whatever. This only covers those employed, i.e they have to get a wage, so you have to pay at least minimum wage. Somebody unpaid isn't usually covered so, while I agree it is an excuse, it does have some basis.
They don't mean the insurance companies have to cover liability for mistakes made. A personal insurance policy against accidents at home or while engaging in social activities usually doesn't cover accidents in the workplace, but you could contact an insurance broker to check what is available.
Employer's liability covers employees. Public liability covers members of the public. Issue arises when a 'member of the public', who isn't an employee, is working and the injury is as a direct result of the work they are doing. As always the detail is in the small print and usually only comes to light if you have to make a claim.
Any students I have in on work experience are always covered by their school or college, but not by my insurance.