Fair comment. I based my opinion on the snippets around at the time suggesting they had prosecuted her because she was famous and the implication if the same had happened to an unknown the case would not have gone to court.
The reviewing lawyer would have to apply what’s referred to as the public interest test as part of the decision process. Given this was a domestic violence case, the CPS, rather than the police, are obliged to make the charging decision.
The police are allowed to make some charging decisions, and the process is the same. First, a case has to meet the evidential test - there has to be a realistic prospect of conviction. If that test is met, the case then has to be in the public interest to prosecute. As someone who has made countless charging decisions myself, I can say without hesitation that the public interest test in a case involving someone in the public eye is likely to be an absolute nightmare.