Does the "keystone army" trope in medieval sources reflect reality?

In medieval chronicles, it's quite common to read that Army A was thrashing Army B six ways to Sunday, in fact most of Army B had already fled the field, but then Army B gets lucky, takes Army A's general out with an audacious move or a Hail-Mary shot, and Army B panics, melts away and gets utterly routed.

Now, I can see that happening when the general in question is the claimant on which the whole war is based. Or if it's a remarkably charismatic individual, in the vein of Napoleon or Alexander. Or even if it's one of those peasant levy armies.

But it stretches credibility to think that armies made up of disciplined, battle-hardened veterans who know all too well what happens when an army routs, who are in proper battle formation and clearly hold the upper hand on the field, would break ranks in panic and get themselves slaughtered by the thousands just because their middling nobody of a general got sniped.

So, my question is: did such narratives in medieval chronicles accurately reflect the flow of battle, or were chronicles simply pinning the outcome on a particularly salient event?