It's not as much hiring as it is firing or disciplining a paramedic. There are risks, albeit I don't think they're that strong. Most EMS medical directors are not employees of the agency they direct. Therefore, as independent contractors, they can be held liable personally for their actions. This is why it's highly recommended that EMS medical directors carry an EMS specific malpractice policy. NFP offers one (NAEMSP endorses it). I have it and it covers not only malpractice for clinical care I provide in the field, but also malpractice for what the paramedics do, if I teach them something that is incorrect, etc. There is a built-in D&O policy that protects me for the boards that I serve on (regional EMS authority committee, state medical directors committee that determines scope of practice, etc.). I also have a general liability policy in case my actions cause the county's computer networks to go down, I damage their property, etc. It's typical for most businesses, but outside the scope for general medical malpractice insurance. This is why EMS insurance is necessary.
On another note, some states allow medical directors who volunteer to have sovereign immunity. If you volunteer your time, you should check with your state.