Private Lynch was part of a unit whose mission was to maintain the vehicles of the US Army's 3rd Infantry Division, which at the moment was pushing on to Baghdad at breakneak speed, bypassing serious points of resistance. One of these places was the town of Fallujah. As the advance elements of the 3rd Infantry Division approached the city, they found no resistance: the Iraqi army unit assigned to protect the town, like much of the Iraqi army, wisesly decided to desert their posts.
In their place came the Arab irregulars. There are many other words that can be used to describe them: holy warriors, jihadists, insurgents...terrorists. As the massive American division rollled by, a special US Marine force was assigned to clear the city. It was into this cauldron that Private Lynch and her unit drove into, instead of around.
It doesn't take a Caesar to ambush a convoy of "soft-skinned" vehicles, and the attacker in a situation like this has an obvious advantage. Private Lynch and her buddies were given the classic "Basic Training", emphasis on basic. While they knew how to fire their rifles, in their suceptibility to the element of surprise they were especially vulnerable for they did not receive, being mechanics, the intense training a combat soldier undergoes in the ability to recover from a shock and deal with the situation.
A short firefight ensued. Several of them were killed, many wounded. While the early reports of the plucky blonde American girl going down like Crocket at the Alamo were innacurate (she does not remember much if anything of the encounter, which may say something about her training, or lack thereof), they're still Americans with guns and so likely did not go quitely. Lynch was probably seriously wounded early on and lost consciousness.
Her attackers did not kill her out of hand likely because they realized she was more useful to their cause alive than dead. She was in critical condition, and so her captors took her to a clinic. The Iraqi doctor who saved her life, realizing her likely fate in the hands of her captors, bravely crossed the lines, so to speak, and got a message through to American forces.
Special forces were callled in, distracted the Arab fighters, nipped in and grabbed Lynch, as everyone got to see on TV.
So in short, the Army left an enemy to its rear for the Marines to deal with, Lynch and her buddies ran smack into those enemies, and they came second place in a firefight with those crazed zealots, their training and/or equipment not being sufficient to fend them off.
The training issue is a bit of a red herring though. It's not really practical to train your support troops up to the level of combat troops - unless you're a relatively small, specialized group like the US Marines - every person a rifleperson
Jessica Lynch was supposed to be protected by the almost indescribable speed and firepower of a American infantry division. If her unit was considered to be under threat, it would have protection, enough protection to make any attacker pause. The point has been made that they are still soldiers, and indeed they are. I seem to remember an episode during at Ypres in 1915 where the Prussian Guard, no less, was beaten off by the cooks and servants of a headquarters company.
Would a couple days of convoy ambush drills have helped Lynch and her friends? Perhaps. We'll never know, but more training is usually better than less.