I agree that the title is disrespectful. After all, you possess a EMT license. An alternate title should be EMT/Firefighter Intern.
I would look a bit closer at the position. Ambulance operators (AO's) typically aren't employed by the (fire) department, and instead are contracted though an employment agency.
Rationale behind this is:
A) The fire department keeps medics on their fire engines and allows EMT's to 'operate' the ambulance, transporting BLS patients without tying up medics.
B) At a fraction of the cost, the fire department can operate a fire department ambulance, with distinct ambulance personnel, not open to work on the fire apparatus, and have the ambulance operators exempt from work comp, insurance costs, and limit fire scene activities. *One must remember that pension, overtime, etc. eats at as fire departments budget. The starting pay isn't all that great.
C) Fire house chores/responsibilities often get relegated to 'low man on the totem pole'; ie. AO's versus full-time/FD personnel
The benefits:
A) Great work location
B) Experience and possible leg up when hiring for full time firefighter
C) Resume builder