I've seen several members of the princely family when I've been in monaco. As far as I remember right now I've seen once Caroline on her own, twice Caroline and Ernst, once Ernst and Pierre, and one last time little Alexandra with someone I didn't recognize, maybe a nanny. In maybe half of these occasions they were accompanied by very conspicuous body guards, so I can assure you that they do use body guards in Monaco.
Where exactly did I say they didn't use bodyguards in Monaco? I said there was no need for bodyguards in Monaco, I didn't say they failed to use them.
My Grandparents have lived in Monaco for 40 years [actually in the same building as Princess Stephanie in Fontvieille] so I generally have spent a lot of time there growing up & I've seen all 3 of the Casiraghis [individually] without security. On the other hand, everytime I've seen Prince Albert he's had security & Stephanie's kids seem to always have security.
I've also seen Charlotte twice in London without security & seen Andrea on lower 5th Av in New York coming out of 'Otto' the pizza restaurant & he had zero security.