A friend recently took a recreational scuba instructor course from ANDI and was told that my agency (fire department) must have a dive master on every dive, with insurance, regardless whether it's a training dive or an actual callout.
...Was this a misunderstanding, or are we in violation or some rules?
The person who made this statement is either misquoted or not aware of factual information. (And I agree with Gary, this is common when recreational agencies dabble in PSD...)
The NFPA* has drafted a Public Safety Diving standard and compliance is voluntary. While there can be civil liability issues there is no mandate that requires a certified dive master on each dive operation. The NFPA standard can be viewed on-line at:
http://www.nfpa.org/freecodes/free_access_agreement.asp?id=100608
The portion that addresses this issue reads...
13.2* Level II General Requirements.
In addition to the requirements of
Level I, candidates shall possess accepted advanced open water SCUBA
certification from a nationally recognized agency. At the entry level, and for
any specialties utilized by an organization at Level II, the AHJ shall ensure
provision of qualifying in that specialty by a nationally recognized certifying
agency. The curriculum for such qualification shall be oriented toward
the needs and operational requirements of public safety diving as defined herein.
13.2.5
Supervise, coordinate, and lead dive teams during operations, given
incident checklists, dive checklists, maps, topographic surveys, charts, and
pre-dive/post-dive medical evaluation checklist, so that teams are managed,
personnel are supervised, hazards are assessed and identified, safety and
health of team is ensured, qualifications/abilities of divers are verified, predive
briefing is conducted, and post-dive medical evaluation and briefing is
performed.
(A)
Requisite Knowledge.
“Divemaster” level knowledge; knowledge of
supervisory practices, dive tables, emergency procedures, communications
procedures, local protocols, and pre-dive safety checks.
A.13.2
The committee is of the opinion that Advanced Open Water
certification provided by most nationally recognized certifying agencies
(agencies associated with the Recreational SCUBA Training Council) build
an acceptable foundation for the basic SCUBA skills required for dive rescue
technician. These courses do not, however, offer all of the skills required to
meet these standards, and further training and experience in special hazards
expected to be encountered in the AHJ’s territory should be sought.
Examples of nationally recognized certifying agencies include PADI,
NAUI, YMCA, SSI, and DRI. Candidates should have experience diving
in various environments by taking additional specialties. Examples of
specialties include ice, current, hazardous materials, dry suit, and lifting
operations. Annual confirmation of these skills should be performed to
ensure continued competency. An example of these skills can be found in
Figure A.13.2 on the following page.
Candidates should demonstrate leadership skills similar to that of a
“Divemaster” as defined by the Recreational SCUBA Training Council. The
dive rescue technician should have documented substantial dive experience in
varied environments and have the ability to supervise and lead others. These
personnel should also be able to employ checklists to identify pre- and postdive
needs.
The standard does not require a certified divemaster, it requires that the "Level II diver" have "divemaster level knowledge." And while the NFPA standard may set requirements, compliance is voluntary. For someone to state otherwise indicates that they do not have knowledge of the standard and may cause some to question their ability to teach public safety diving.
Along the same lines, I would suggest that everyone be VERY leery of anyone who claims that they offer an "NFPA compliant" program or that their training "meets the NFPA standard." Anyone who states this doesn't know the standard well enough since the Authority Having Jurisdiction (AHJ) is the only one who can establish what training their personnel are required to have. The AHJ determines the standard, NOT the commercial training agency. I.E., the AHJ can require that their PSDs are also EMTs; is the commercial dive training vendor also qualified to teach EMT class?
Glad to set the record straight...
NOTE: Regarding the NFPA, the PSD Standard is not applicapable to Fire Departments only. It applies to ALL public safety dive teams. The body that certifies the NFPA code development process is the American National Standards Institute (ANSI) and ANSI is the official U.S. representative to the International Organization for Standardization (ISO). 
