A former champion shooter writes:

would say it is impossible to clean the Browning pistol when it is
loaded. To clean a gun it means to clean the inside of the barrel and
cartridge chamber. The explosive behind the bullet corrodes the rifling
inside the barrel. Cleaning a gun means to clean inside the gun, not
the outside. Without knowing any safety rules, what is the first thing
to do to clean the pistol? Remove the magazine that holds the bullets.
It is semi-automatic so the only way to get the bullets in or out is
via the magazine. After you pull the trigger it throws the empty
cartridge out through the hole in the side of the pistol. How can you
clean the barrel and chamber if you don’t remove the magazine? You
can’t. After you have finished cleaning the pistol what do you do? Yes,
put the cartridge magazine back into the pistol. So Private Kovco had
finished cleaning the pistol. The Browning dates from WWII and is heavy
… it has been modified to lighten it for today’s troops. The Canadian
Army also uses it. So if it was easy for the pistol to be discharged or
anyone else was killed accidentally, why has it been used for more than
60 years?

A retired infantry officer writes:
the soldier was using the 9mm Browning pistol (the one with the
magazine in the pistol grip) to complete step 3 “fire the action”, it
requires an “empty” to be placed back on the pistol for that trigger to
be fired to complete step 3, thus rendering the pistol safe. This can
be done with a loaded magazine too (not recommended as it is an illegal
short cut as most magazines on operations are loaded), but the weapon
after it is cocked to expend any round from the chamber (step 2) the
working parts must be allowed to go forward by releasing a catch (a
catch separate from the safety catch) before the mag is put on. The
soldier may have done this by released the working parts AFTER a loaded
mag was put on which would chamber a new round and that round would be
fired when the trigger is pressed. This does not explain why the pistol
was pointed at his head when he pulled the trigger.

A competitive sporting pistol shooter writes:
should NEVER attempt to clean a loaded gun! He would have known that
and if it was an accident, he broke one of the most fundamental rules
of firearm safety by not making sure the gun was unloaded before
attempting to clean it. In my opinion it beggars belief that a soldier
as experienced in weapons as he would have been would have been so
careless as to ignore this basic rule. The fact that he was shot in the
head also indicates to me that something is amiss, as a semi-automatic
pistol such as the Army’s 9mm Browning pistol needs to be partially
disassembled in order to be cleaned effectively, thus rendering it
inoperable and there is NEVER a need to point it at one’s head whilst
doing so.