I'm not sure Chelsy didn't want the spotlight. I believe the version that claims she broke up with Harry because he cheated on her.

And Cressida had broken up with guy she eventually married then immediately started a relationship with Harry. Rebound relationships usually don't work. Cressida has also been reported to have said that Harry wasn't a nice person.

I think both women used the spotlight excuse as the reason for the breakup to avoid badmouthing Harry and/or because it showed themselves in a good light.