Well, her dad had almost been killed by Italo-Norman lances back when Robert Guiscard tried to expand across the Adriatic. The Byzantines were enough on the receiving end of "Frankish" lances to have a healthy respect for them (curio detail: conversely the heavy maces of some Byzantine cavalry were apparently widely respected and feared).
One would assume that at least the early-pattern knights (you know, the ones who weren't much more than lords' household mercenaries) were by necessity heavily engaged in scouting and skirmish duties - there normally weren't too many other decent mounted troops beside them available anyway. And let's not underestimate the ability of knights to make themselves troublesome to horse-archers - after all, the Templars started out as volunteer guards for pilgrim caravans against "Saracen" raiders, many of whom were no doubt enterprising Turkic tribesmen out to improve their finances (not that horse archers were rare mong the more settled peoples of the region either)... A mail-clad fellow with a big shield is apparently annoyingly resistant to arrows, although his horse may be another story.
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