Without knowing which data set he was using I can't be sure of what all he was including on his accidental death tally; there is a DOD and a National Archives set of statistics, and for example one counts drownings towards the accident total, the other does not. In either case the discrepancy is roughly 3,000, and are accounted for elsewhere.

What I can specify is what types of accidents were occurring, and what types generally occur in a warzone.

Accidental deaths include just that - accidents: events which occurred without direct hostile intent. Among these numbers are events like the deaths of 44 sailors, caused when a flare locker onboard the USS Oriskany was ignited by two servicemembers who had been firing flares at each other for fun.

Other events which were included were non-combat crashes of aircraft, which could occur both in the country or at sea. For example in August of 1965 the DOD reported 52 servicemembers killed in aircraft accidents at sea. While they don't describe in the database the nature, one could reasonably conclude this to be the result of a transport aircraft going down.

A combat zone is filled with heavy equipment; add in long term stress and lack of sleep and you have the perfect environment to breed complacency - and human error can be even more dangerous than mechanical failures, as there are often no redundant systems in place to offer a fail safe. The common ones in this department would be vehicle accidents, negligent discharge of weapons, electrical injuries, accidental drowning, accidental (un)friendly-fire, structure failures, and others along that line.

Finally, the DOD statistics often include illness and disease in the total as accidental deaths. Historically, these had been the most dangerous threats to armies in the field and, considering the environment, the military did a decent job of keeping these numbers down (938). The common culprits would be malaria, dysentery, and other similar maladies.

You can view the NARA Stats here

And y The DOD stats for Vietnam and other conflicts here

From the US Archives:

Casualty Category	Number
Accident	9,107
Declared Dead	1,201
Died of Wounds	5,299
Homicide	236
Illness	938
Killed in Action	40,934
Presumed Dead (Remains Recovered)	32
Presumed Dead (Remains Not Recovered)	91
Self-Inflicted	382
TOTAL	58,220

Broken down between hostile and non-hostile:

Type	Number
Hostile	47,434
Non-Hostile	10,786

So from there, you can see that the roughly 9,100 deaths listed as accidents and 10,800 non-hostile deaths is like what the author mentions as 'accidents'

The 10,786 non-hostile deaths is made up of Accidents + Homicide + Illness + Self-Inflicted + Presumed Dead

The 2016 Department of Defense Dictionary of Military and Associated Terms update uses the term 'nonbattle injury' now, instead of non-hostile. It is defined as:

A person who becomes a casualty due to circumstances not directly attributable to hostile action or terrorist activity. Also called NBI

Also, disease and nonbattle injury is defined as:

All illnesses and injuries not resulting from enemy or terrorist action or caused by conflict. Also called DNBI.

Accidents - such as aviation accidents, motor accidents, training accidents, etc. would all be counted as such.

This isn't a small matter either. For instance, in World War II, a grand total of 4,832 officers + officer candidates + enlisted were killed in action in air combat for the US Navy.

In aviation accidents, however, a grand total of 11,699 officers + officer candidates + enlisted were killed in the US Navy. That's right, nearly 3 times more people died in aviation accidents than in actual aerial combat (no one ever said landing on an aircraft carrier was easy...)

Source: US Navy Personnel in World War II: Service and Casualty Statistics

Now, as far as the types of accidents that would be included in Vietnam:

• Aviation accidents. One that immediately comes to mind is the Forrestal Fire, in which over 130 sailors were killed
• Equipment/vehicular accidents. In The Vietnam War by James E. Westheider, he documents "a man being run over and killed by a tug, a large vehicle used to tow aircraft" here:

"He stopped off the airplane, his first day in Vietnam, walked right in front of the tug which this guy was driving backwards and wasn't watching where he was going and just peeled him like a grape... It was more horrifying than watching the enemy killed"

Other types of aviation accidents were noted:

He also witnessed an F-105 come in too low and clip the wheel shack, a small observation shed where someone with binoculars checked to make sure that the landing gear retracted correctly on outgoing planes, killing the pilot

A C-147 stalled on takeoff and crashed, killing all seven on board

Other notable accidents:

A C-5, in Operation Babylift, crashed in April 1975 outside Tan Son Nhut Air Base in South Vietnam. 11 Air Force personnel, 35 Defense Attache Office employees, and 78 children were killed. 173 others survived the crash.

In John Schlight's "A War Too Long: The USAF in Southeast Asia 1961-1975", he notes that 514 aircraft were lost due to accidents out of the 2,251 aircraft lost by the Air Force.

Unfortunately, accidents do still happen, and they still make up a large chunk of losses. Using Iraq War statistics, out of 4,411 total deaths, 930 were categorized as non-hostile - a full 21% of deaths.

If you break it down further here:

Type	Number
Accident	566
Illness	94
Homicide	36
Self-Inflicted	223
Undetermined	11