To me the statement reads that as parents they are totally fine sending their children to this boarding school (even though it has systemic bullying issues), however, their position as crown prince couple makes them think twice as it might damage their credibilty.
Not a very encouraging starting point imho.
What I get from the statement is what I already assumed, i.e. that Christian is very happy at Herlufsholm and excited to go there. Honestly, why wouldn't he feel like that? As a male who can relate to those experiences, I am pretty sure that Herlufsholm must be very fun for a 16-year-old boy with Christian's profile (usually kids like him are not the ones at the receiving end of bullying incidents).
But, although they don't want to upset their kids (both Christian and now apparently Isabella), F&M, as you said, are also worried, as the CP couple, about the public implications of keeping them at Herlufsholm. In the end, it will all depend on Herlufsholm being able to reform or, at least, looking like it is doing something concrete to change its culture and end the type of incidents that have been uncovered. My impression is that F&M will push it to the limit and will take action only if their position becomes untenable.