I think it betrays a pretty limited understanding of design, to declare a design task impossible because color-coordination can't be scoped in. Prioritizing aesthetics over function usually defeats both.
I'm gonna take your word for it tho and will use the complain button on that Bulgari page to let them know their solution "betrays a pretty limited understanding of design" and they will need your more competent service. /s
The browser scrollbar shouldn't be part of the corporate/brand identity any more than the browser menu, address bar or navigation buttons. Navigation belongs to the user, not the webpage designer.