Don't know.
It could be anything really. If they feel so strong, why not make a complaint about the bullying, if it happened. I know I would have my knickers in a twist it that happened to my DC, so would most parents.
It is possible that KM was unsettled as the HM says. She was a popular hockey player at prep, likely with recognition and praise. She comes to a school with 'alpha girls' great at sport, academics and generally full of confidence. Maybe they just did not rate her - there is no substance to this bullying accusation, like what actually took place. Was she being shoved, what pranks were played on her etc. The best we can say is that girls being cliquey is not new, they may take some time to bring in newcomers. She probably was not the only one who was new, and that may take more than a term to break into.
Nowadays, you have to register your DC 2yrs in advance for Marlborough, I doubt that was the case then, but it was still a very exclusive school. Eugenie went there, it was also labeled the 'first wives club', with the likes of Samantha Cameron, Sally Bercow and other prominent wives having attended. My guess is that a contact of the Middletons arranged or made then aware of a space may available mid school year if you know or talk to certain people- which is rather unusual. Since she was not particularly happy at her school they took the leap.
At either schools, KM herself would not have had the clout to bully anyone.